Question

Find the absolute maximum value for the function f(x) = x^2 − 4, on the interval [–3, 0) U (0, 2].

Answer 1

Answer:

5

Step-by-step explanation:

The function $y=x^2 -4$ is

• decreasing for all $x\in [-3,0);$
• is increasing for all $x\in (0,2]$

(see attached diagram for details).

The maximum value of the function is at endpoints -3 or 2. find y(-3) and y(2):

$y(-3)=(-3)^2-4=9-4=5\\ \\y(2)=4^2-4=0$

So, the maximum value is 5.