AP Calculus AB Midterm Review.

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Presentation transcript:

AP Calculus AB Midterm Review

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

Limits; sinx/x

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

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

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

Limit definition of derivative

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

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

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

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.

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

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

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.

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

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

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

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

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