Given:
f'(2) = 0 and f'(5) = 0
Thus, we have:
f'(x) = 0 at x = 2 and x = 5
Let's classify the critical points as relative maximums, relative minimums or neither.
Now, we have the following:
• When x = 2, the function f'(x) does not change its sign. Hence, x = 2 is neither a relative maximum nor relative minimum point.
• When x = 5, the sign f'(x) changes sign from positive to negative. Since the sign changes from positive to negative, hence x = 5 is a relative maximum point.
ANSWER:
• Relative maximum: x = 5
,
• Neither relative maximum nor minimum: x = 2
