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AP Calculus AB Midterm Review

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If , then is A. B. C. D. Implicit Differentiation

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Limits; sinx/x

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If , then Chain rule, exponential & trig derivatives; Unit Circle

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**Write the equation of the line tangent to at**

Equation of tangent line

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**has vertical asymptote(s) at**

The graph of has vertical asymptote(s) at Asymptotes

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**Limit definition of derivative**

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**concave up? For what values of x is**

Derivatives; 2nd derivatives & concavity

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**If f(1)=2 and f’(1)=5, use the equation of the tangent line to **

the graph of f(x) at x=1 to approximate f(1.2). Finding & using equation of tangent line

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**The graph of f ‘(x) is shown at right. **

Which of the following could be the graph of f (x)? f ‘(x) A. B. C. D. E. Graphs of f ‘ and f

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**statements is true about the figure at right?**

Which of the following statements is true about the figure at right? -7 -3 5 A. exists B. exists C. Limits (graphically), continuity; MVT D. E.

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**1 2 3 4 How many points of inflection are there for the function ?**

on the interval 1 2 3 4 Second derivatives, including Chain Rule & trig; Points of Inflection

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**GRAPHING CALCULATOR ALLOWED . Consider the function**

For what value(s) of x is the slope of the tangent line equal to 5? Derivative as slope of tangent line; using graphing calculator to solve equations

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**A pebble thrown into a pond creates circular ripples such that **

the rate of change of the radius is 6 cm/sec. How fast is the area of the ripple changing when the circumference is cm? sq.cm./sec. sq.cm./sec. sq.cm./sec. Related rates sq.cm./sec. sq.cm./sec.

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**0.396 0.955 1.350 1.910 Undefined GRAPHING CALCULATOR ALLOWED**

Find the average rate of change of on the interval . 0.396 0.955 1.350 1.910 Undefined ARoC; secant

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**In the figure shown at right, which of the following is true?**

B. C. D. E. Limits, including one-sided; differentiability; MVT The average rate of change of f(x) on [1,3] equals

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**A function f(x) is continuous on [a,b]. Which of the following **

must be true? f has a maximum on [a,b] B. f has a point of inflection on [a,b] for at least one c in the interval [a,b] C. D. for at least one c in the interval [a,b] E. f has a critical value on the interval (a,b) Absolute extrema; MVT; critical values

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If , then Relationship between velocity & acceleration; ln derivatives; evaluating derivatives

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CHALLENGE! Limit definition of derivative; derivative of ln; derivative of derivative

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DO NOW: Find where the function f(x) = 3x4 – 4x3 – 12x2 + 5

DO NOW: Find where the function f(x) = 3x4 – 4x3 – 12x2 + 5

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