Applied Max and Min

Question

Find the absolute maximum value of the function 

Options:

1. 0
2. 1
3. 2
4. 3

Answer 1

Why not just write the equations?

f(x) = x² + 2, 0 ≤ x ≤ 1

f(x) = -x, x > 1

For the 1st segment, take the first derivative and set = to 0

f' = 2x = 0

x = 0

By inspection, this is a minimum. The maximum occurs when x = 1

In the second equation, x is negative, so the answer is 1