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AP Calculus AB Midterm Review.

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Presentation on theme: "AP Calculus AB Midterm Review."— Presentation transcript:

1 AP Calculus AB Midterm Review

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

3 Limits; sinx/x

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

5 Write the equation of the line tangent to at
Equation of tangent line

6 has vertical asymptote(s) at
The graph of has vertical asymptote(s) at Asymptotes

7 Limit definition of derivative

8 concave up? For what values of x is
Derivatives; 2nd derivatives & concavity

9 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

10 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

11 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.

12 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

13 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

14 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? Related rates

15 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

16 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

17 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

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

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

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