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| 6542604251 | What conditions must be to satisfied for the Mean Value Theorem to be valid? | f(x) is continuous in the interval [a, b] and differentiable in the interval (a, b) | 0 | |
| 6542604252 | If the appropriate conditions are satisfied, what does the Mean Value Theorem guarantee? | There is at least one point c in the interval (a, b) at which f'(c) = [f(b) - f(a)] / [b - a] | 1 | |
| 6542604253 | Limit | A limit is the value that a function or sequence "approaches" as the input or index approaches some value. | 2 | |
| 6542604254 | Quotient rule? | (vu'-uv')/v^2 | 3 | |
| 6542604255 | When does a derivative not exist at 'x' (with a graph)? | Corner Cusp Vertical Tangent Discontinuity | 4 | |
| 6542604256 | What does a cusp look like? | When a function becomes vertical and then virtually doubles back on itself. Such pattern signals the presence of what is known as a vertical cusp. |  | 5 |
| 6542604257 | What does a Vertical Tangent look like? | vertical tangent image | 6 | |
| 6542604258 | Difference Rule | Function - f - g Derivative - f' − g' |  | 7 |
| 6542604259 | Reciprocal Rule | Function 1/f Derivative −f'/f2 | 8 | |
| 6542604260 | Chain Rule (Using ' ) | Function f(g(x)) Derivative f'(g(x))g'(x) | 9 | |
| 6542604261 | Product Rule | Function - fg Derivative - f g' + f' g |  | 10 |
| 6542604262 | Chain Rule (Using d/dx) |  | 11 | |
| 6542604263 | What does a Corner look like? | Corner at (17, 600) and (18, 530) |  | 12 |
| 6542604264 | What does a jump discontinuity look like? |  | 13 | |
| 6542604265 | Power Rule | Function - x^n Derivative - 〖nx〗^(n-1) |  | 14 |
| 6542604266 | Quotient Rule | Function (f/g) Derivative | 15 | |
| 6542604267 | Sum Rule | Function - f + g Derivative - f' + g' | | 16 |
| 6542604268 | How do I find an equation of a line tangent to a curve | 1.) Calculate the slope of a secant through P and a point Q nearby on the curve. 2.)Find the limiting value of a secant slope (if it exists) as Q approaches P along the curve. 3.)Define the slope of the curve at P to be this number and define the tangent to the curve at P to be the line through P with this slope. | 17 | |
| 6542604269 | Derivative rules | 18 | ||
| 6542604270 | Power rule | X^2 --> 2X^2-1 ---> 2X | 19 | |
| 6542604271 | How to find derivative? | Solve a problem for (dy/dx). Solutions may involve power, product, chain or quotient rule. | 20 | |
| 6542604272 | How do we handle negative exponents? | Negative exponents are moved to the bottom of a fraction to make the exponent positive. When finding derivatives, it's easier to solve when you put a factor from the denominator of the fraction to the top with a negative exponent and use the power rule. | 21 | |
| 6542604273 | Derivative of tangent inverse |  | 22 | |
| 6542604274 | If the definition of the derivative is recognized, what does it guarantee? | 23 | ||
| 6542604275 | Types of discontinuity | Removable Discontinuity: when a point on the graph is undefined or does not fit the rest of the graph (there is a hole) Jump Discontinuity: when two one-sided limits exist, but they have different values Infinite Discontinuity: | 24 | |
| 6542604276 | Product rule? | uv'+vu' | 25 | |
| 6542604277 | Rate of Change | Expressed as a ratio between a change in one variable relative to a corresponding change in another. When the function y=F(x) is concave up, the graph of its derivative y=f'(x) is increasing. When the function y=F(x) is concave down, the graph of its derivative y=f'(x) is decreasing. | 26 | |
| 6542604278 | Rules of Piecewise Functions | A Piecewise function is made up of sub-functions that apply to a certain interval of the main function's domain. First look at the conditions on the right to see where x is. Then just plug that number into the equation. |  | 27 |
| 6542604279 | How do you interpret a velocity graph to determine speed? | Velocity is the first derivative of position. In order to graph speed from velocity then you need to find the derivative of velocity from the graph. In order to do that you need to reflect the negative terms across the x-axis making them positive. |  | 28 |
| 6542604280 | Chain Rule | (F o G)' (x) = f'(g(x)) *g' (x) | 29 | |
| 6542604281 | What are discontinuities? When are limits nonexistent? | Limits dont exist when the values from the left and righ are3 no equal | 30 | |
| 6542604282 | What are the derivatives of trig functions? | sin(x) = cos (x); cos (x) = -sin(x); tan(x) = sec^2(x) | 31 | |
| 6542604283 | Unit Circle | Since C = 2πr, the circumference of a unit circle is 2π. A unit circle is a circle with a radius of one. Frequently, especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system. |  | 32 |
| 6542604284 | Find the derivative of the square root of f(x) | The derivative of the square root of a function is equal to the derivative of the radical divided by the double of the root. |  | 33 |
| 6542604285 | What are the 1st and 2nd derivatives of displacement? | 1st derivative is velocity and the 2nd is acceleration. These are found by identifying the slope of displacement to find velocity, and slope of velocity to find acceleration | 34 | |
| 6542604286 | Recognizing Implicit Differentiation | Used when an equation contains a variable besides x For example: 3x + 4y = 12 derivative of y= dy/dx | 35 | |
| 6542604287 | How do you find a Local Extrema? | 1. Find the first derivative of f using the power rule. 2. Set the derivative equal to zero and solve for x. x = 0, -2, or These three x-values are the critical numbers of f. | 36 | |
| 6542604288 | how to find identify the original function of a graph | 37 | ||
| 6542604289 | Mean value theorem for derivatives | if f(x) is continuous over [a,b] and differentiable over (a,b), then at some point c is between a and b. |  | 38 |
| 6542604290 | What is the derivative of a position function? How do you find where the function is decreasing? | Speed/Velocity. The function is decreasing when y' is negative (below the x-axis) | 39 | |
| 6542604291 | Second Derivative | Take first derivative. Then, find the derivative of the first derivative. f'(x), then f''(x). | 40 | |
| 6542604292 | Derivative of e^x | e^x * derivative of argument | 41 | |
| 6542604293 | How do you determine the end behavior model of a polynomial function going to positive or negative infinity? | take the variable with the largest exponent and substitute the variable with the limit | 42 | |
| 6542604294 | Definition of a limit | definition of a limit | 43 | |
| 6542604295 | Product Rule | u*v' + v*u' | 44 | |
| 6542604296 | Implicit differentitation | (image) | 45 | |
| 6542604297 | The derivative of the function f at the point x=a is the limit... if the limit exists. | picture on email | 46 | |
| 6542604298 | Power rule | | 47 | |
| 6542604299 | How do you find the absolute extrema of a function? How can you find the absolute extrema of a function on an interval with end points? | Find critical points by funding where the first derivative is 0 or undefined, then plug in end points to f(x) and critical points to find extrema. | 48 | |
| 6542604300 | Power Rule | If function f is f(x) = x^n, where n is any integer, then f' (x) = n·x^n-1. | 49 | |
| 6542604301 | How do you find the limit of a piece-wise function? | Step 1 Evaluate the one-sided limits for each function. Step 2 If the one-sided limits are the same, the limit exists. If the one-sided limits are different, the limit doesn't exist. | | 50 |
| 6542604302 | Derivative of y | dy/dx | 51 | |
| 6542604303 | How do you find the derivative of an inverse function? | If f and g are inverse functions, then f'(x)=1/(g'(f(x)) | 52 | |
| 6542604304 | When can removable discontinuities be fixed? | Removable discontinuities can be "fixed" by re-defining the function. | 53 | |
| 6542604305 | Finding the vertical asymptote | When the denominator of the function equals 0. | 54 | |
| 6542604306 | When are limits nonexistent? | Jump Discontinuities: both one-sided limits exist, but have different values. Infinite Discontinuities: both one-sided limits are infinite. Endpoint Discontinuities: only one of the one-sided limits exists. Mixed: at least one of the one-sided limits does not exist. | 55 | |
| 6542604307 | Increasing Functions | Where the graph of the first derivative shows the original function being continuous, differentiable and increasing. | 56 | |
| 6542604308 | What is point-slope form? |  | 57 | |
| 6542604309 | f^-1 represents what? | An inverse function | 58 | |
| 6542604310 | What must be true for a limit to exist? | limit from the left = limit from the right | 59 | |
| 6542604311 | What is an inflection point? | A point of a curve at which a change in the direction of curvature occurs. |  | 60 |
| 6542604312 | Where can you not draw a tangent line? | A Corner | 61 | |
| 6542604313 | What does a tangent line look like? | A straight line that hits a curve at exactly one point |  | 62 |
| 6542604314 | How to find a vertical asymptote | 1. Set the denominator equal to zero 2. Simplify the fraction 3. Cancel out like terms on the top and the bottom | 63 | |
| 6542604315 | How do you move a term from the denominator to the numerator? | Make the power of the denominator negative than multiply the denominator by the numerator | 64 | |
| 6542604316 | Extreme Value theorem | If f is continuous over a closed interval, then f has maximum an minimum values over that interval. | 65 | |
| 6542604317 | critical points | Is where there is a point in the domain of a function f at which f'=0 or f' does not exist is a critical point of f. *critical points are not always maximum and minimum values. | 66 | |
| 6542604318 | What graph comes as a result of finding the derivative of a speed graph? | Acceleration Graph | 67 | |
| 6542604319 | Derivative of a function in f(x) notation | 68 | ||
| 6542604320 | How do you find the local extrema of a function? | Find the first derivative and set it equal to zero | 69 | |
| 6542604321 | When is a function decreasing? | When the first derivative/ slope is negative | 70 | |
| 6542604322 | When is the second derivative of a function negative? | When the graph of the function is concave down | 71 | |
| 6542604323 | When is the second derivative of a function positive? | When the graph of the function is concave up | 72 | |
| 6542604324 | When is a function increasing? | When the first derivative/ slope is positive | 73 | |
| 6542604325 | What graph comes as a result of finding the derivative of an position/displacement graph in absolute valuation? | Speed Graph | 74 | |
| 6542604326 | Why can't you draw a tangent line on a corner? | You can't draw a tangent line because the tangent line from the left and the right will be going different directions. | 75 | |
| 6542604327 | When is the Vertical asymptotes | lim(x→0) (1/x) |  | 76 |
| 6542604328 | What graph comes as a result of finding the derivative of an acceleration graph? | Jerk Graph | 77 | |
| 6542604329 | What does removable continuity look like? | | 78 | |
| 6542604330 | Chain Rule | We use chain rule to find the derivative of the composition of two functions. formula : dy/dx f(g(x)) = f'(g(x))*g'(x) |  | 79 |
| 6542604331 | Mean Value Theorem | F'(c)= f(b)-f(a)/b-a | | 80 |
| 6542604332 | When is the horizontal asymptotes | lim(x→∞) (1/x) |  | 81 |
| 6542604333 | What graph comes as a result of finding the derivative of a displacement graph? | Velocity Graph | 82 | |
| 6542604334 | What is a secant line? *Used in Mean Value Theorem | A secant line is a straight line joining two points on a function. It is also equivalent to the average rate of change, or simply the slope between two points. The average rate of change of a function between two points and the slope between two points are the same thing. |  | 83 |
| 6542604335 | How do you find a local maxima on a graph? | Set derivative equal to zero and solve for "x" to find critical points. Critical points are where the slope of the function is zero or undefined. |  | 84 |
| 6542604336 | Derivative of sine inverse | 1/sqrt(1-x^2) |  | 85 |
| 6542604337 | Derivative of cosine inverse | - 1/sqrt(1-x^2) |  | 86 |
