AP Calc review

Let f be the function with derivative f′(x)=x^3−3x−2. Which of the following statements is true? A) f has no relative minima and one relative maximum. B) f has one relative minimum and no relative maxima. C) f has one relative minimum and one relative maximum. D) f has two relative minima and one relative maximum.

B) f has one relative minimum and no relative maxima.

Let f be the function defined by f(x)=(x+x^2)e^(−2x). On which of the following open intervals is f increasing? A) (−∞, (−3−√5)/2) and ((−3+√5)/2,∞) B) (−∞,−1) and (0,∞) C) (−∞,−√2/2) and (√2/2,∞) D) (−√2/2,√2/2)

D) (−√2/2,√2/2)

Let f be the function with derivative given by f′(x)=x2−a2=(x−a)(x+a), where a is a positive constant. Which of the following statements is true? A) f is decreasing for −a<x<a because f′(x)<0 for −a<x<a. B) f is decreasing for x<−a and x>a because f′(x)<0 for x<−a and x>a. C) f is decreasing for x<0 because f′(x)<0 for x<0. D) f is decreasing for x<0 because f′′(x)<0 for x<0.

a) f is decreasing for −a<x<a because f′(x)<0 for −a<x<a.

Let f be the function defined by f(x)=12x−x^3. What is the absolute minimum value of f on the closed interval [0,3] ? A) −16 B) 0 C) 9 D) 16

B) 0

CALCULATOR Let f be the function with derivative given by f′(x)=sinx+cos(2x)−π4 for 0≤x≤π. On which of the following intervals is f increasing? A) [0,0.724] only B) [0,0.724] and [2.418,3.142] C) [0,0.253] and [1.571,2.889] D) [0.724,2.418]

B) [0,0.724] and [2.418,3.142]

Let f be a differentiable function with a domain of (0,10). It is known that f′(x), the derivative of f(x), is negative on the intervals (0,2) and (4,6) and positive on the intervals (2,4) and (6,10). Which of the following statements is true? A) f has no relative minima and three relative maxima. B) f has one relative minimum and two relative maxima. C) f has two relative minima and one relative maximum. D) f has three relative minima and no relative maxima.

C) f has two relative minima and one relative maximum.

Let g be the function defined by g(x)=|x|−3|x+1|. What is the absolute maximum value of g on the closed interval [−2,2] ? A) 1 B) −1 C) −3 D) −7

A) 1

Let g be the function given by g(x)=3x^4−8x^3. At what value of xx on the closed interval [−2,2] does g have an absolute maximum? A) −2 B) 0 C) 2 D) 8/3

A) −2

The function f is defined by f(x)=e^(−x )(x^(2)+2x). At what values of x does f have a relative maximum? A) x=−2+√2 and x=−2−√2 B) x=−√2 only C) x=−2 and x=0 D) x=√2 only

D) x=√2 only