Ex 2.8
3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1

The value of the second derivative for is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of is always positive for . That means at there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval .
The function is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.