AP Calculus Help

Question

1. Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0,4]?

a. y= tanx

b. y= tan^-1x

c. y= x² - 16/(x² + x -20)

d. y= 1/(e^x - 1)

2. Which of the following functions of x is guaranteed by the Extreme Value Theorem to have an absolute maximum on the interval [0,2π]?

a. y= 1/(1 + sinx)

b. y= 1/(x² + π)

c. y= x² - 2πx + π²/(x - π)

d. y= |x - π|/x - π

3. Let f be a differentiable function with a domain of (0,5). It is known that f'(x) is negative on the intervals (0,1) and (2,3) and positive on the intervals (1,2) and (3,5). Which of the following statements is true?

a. f has no relative minima and three relative maxima

b. f has one relative minima and two relative maxima

c. f has two relative minima and one relative maxima

d. f has three relative minima and no relative maxima

4. The function f is defined by f(x)= x²e^{-x^2}. At what values of x does f have a relative maximum?

a. -2

b. 0

c. 1 only

d. -1 and 1

5. Let f be the function with derivative f'(x)= x³ - 3x - 2. Which of the following statements is true?

a. f has no relative minima and one relative maxima

b. f has one relative minima and no relative maxima

c. f has one relative minima and one relative maxima

d. f has two relative minima and one relative maxima

Answer 1

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