Analyzing f, f', and f''

Assume this is a graph of f. What can you say about its first and second derivative from x=1 to x=5?

• f'(x) > 0 and f''(x) > 0
• f'(x) < 0 and f''(x) < 0
• f'(x) > 0 and f''(x) < 0
• f'(x) < 0 and f''(x) > 0

Assume this is a graph of f'(x), the first derivative of f(x), on the interval [1,5]. Which of the following statements are true?

• f is increasing from [1,5]
• f is decreasing from [1,5]
• f is concave up (1,5)
• f has a relative max at x=1

Let the following be a graph of f'(x), the derivative of f on the interval [-1,4]
For what value of x does f have a relative maximum

• x=1
• x=0
• x=2
• There is no relative maximum

Let the following be a graph of f'(x), the derivative of f on the interval [-1,4]
For what value of x does f have a relative minimum

• x=3
• x=0
• x=2
• There is no relative minimum

Given this graph of f'(x). On what interval(s) is f concave down?

• (-1,0) U (1,3)
• (-1,1) U (2,4)
• (0,1) U (3,4)
• (0,2)

Given this graph of f'(x). On what interval(s) is f concave up?

• (-1,0) U (1,3)
• (-1,1) U (2,4)
• (0,1) U (3,4)
• (0,2)

Given this graph of f'(x), list all points of inflection of f. 

• x = 0, x = 2
• x = 0, x = 1, x = 3
• x=2
• x=1

Given this graph of f'(x), on what interval(s) is f increasing?

• [-1,2]
• [0,1] U [3,4]
• [-1,0] U [1,3]
• [2,4]

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Let f(x)=3x⁵-20x³, what are the critical values of f?

• 15x⁴-60x²
• x = 2, x = 0
• x = 2, x= -2, x = 0
• x = 4, x = 0

Let f(x) = (1/2)x⁴-4x³, find the points of inflection of f

• 6x²-24x
• x = 4, x = 0
• x = 0, x = 2
• x = 4, x = 3