5.3 MCQ

the graph of f' the derivative of f, is shown above for -2<= x <=5. On what intervals is f increasing?

• [-2,1] only

• [-2,3]

• [3,5] only

• [0,1.5] and [3,5]

• [-2,-1], [1,2] and [4,5]

the first derivate of the function f is defined by f'(x) = sin(x^3-x) for 0<= x <=2. on what intervals is f increasing?

• 1 <= x <= 1.445 only

• 1 <= x <= 1.691

• 1.445 <= x <= 1.875

• 0.577 <= x <= 1.445 and 1.875 <= x <= 2

• 0 <= x <= 1 and 1.691 <= x <= 2

the figure above shows the graph of the polynomial function f. for which value of x is it true that f"(x) < f'(x) < f(x) ?

• a

• b

• c

• d

• e

let g be the function given by g(x) = integral of x to 1 100(t^2-3t+2)e^-t^2 dt. which of the following statements about g must be true?

I. g is increasing on (1,2)

II. g is increasing on (2,3)

III. g(3) > 0

• I only

• II only

• III only

• II and III only

• I, II, III

The graph of y = f(x) is shown in the figure above. on which of the following intervals are dy/dx > 0 and d^2y/dx^2 < 0 ?

I. a<x<b

II. b<x<c

III. c<x<d

• I only

• II only

• III only

• I and II

• II and III

the graph of f', the derivative of the function f, is shown above. which of the following statements is true about f'?

• f is decreasing for -1 <= x <= 1

• f is increasing for -2 <= x <= 0

• f is increasing for 1 <= x <= 2

• f has a local minimum at x = 0

• f is not differentiable at x = -1 and x = 1

let g be a twice-differentiable function with g'(x) > 0 and g"(x) > 0 for all real numbers x, such that g(4) = 12 and g(5) = 18 of the following, which is a possible value for g(6)?

• 15

• 18

• 21

• 24

• 27

if g is the function given by g(x) = 1/3 x^3 + 3/2 x ^2 - 70x + 5, on which of the following intervals is g decreasing?

• (-infinity, -10) and (7, infinity)

• (-infinity, -7) and (10, inifinity)

• (-infinity, 10)

• (-10,7)

• (-7,10)

the graph of f', the derivative of the function f is shown above. on which of the following intervals is f decreasing?

• [2,4] only

• [3,5] only

• [0,1] and [3,5]

• [2,4] and [6,7]

• [0,2] and [4,6]

if f'(x) > 0 for all x, and f"(x) < 0 for all x, which of the following could be a table of values of f?

• f(x) = 4,3,1

• f(x) = 4,4,4

• f(x) = 4,5,6

• f(x) = 4,5,7

• f(x) = 4,6,7