Mathematics

Problem

Let

f(x)=x^{3}-6x^{2}+9x

for

0\le x \le 5

. Determine the

x

-coordinate at which

f

attains its absolute maximum on the interval

[0,5]

. a)

x=1

x=4

x=5

x=3

Intuitive explanation

The key is to remember that absolute extrema on a closed interval occur either at critical points (where $f'(x)=0$ ) or at the endpoints. Find where the derivative equals zero by factoring, then evaluate $f$ at those critical points and at $x=0$ and $x=5$ to compare. Whichever location gives the largest output is your answer.

Intuitive explanation

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