Question

The graph of f ′(x), the derivative of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 6, find the absolute maximum value of f (x) over the interval [0, 3].
a) 0
b) 8
c) 10
d) 16

Answer 1

We are given graph of f'(x). f(0)=6
We need to find the absolute minimum value of f(x) over interval [0,3]
First we will see the graph of f'(x) over interval [0,3]
f'(3)=3
f'(0)=0
Thus, f'(x) is decreasing
x=0 is critical point of the function f(x) because f'(0)=0
We will get absolute maximum/minimum at x=0. f(x) >0
Hence, f(0) is absolute minimum at x=0 , Absolute minimum = 8

This might be right.

Answer 2

f(x) is increasing sorry not decreasing

Answer 3

well the answer is 8

Answer 4

I mean 10