What is the extreme f(x)=(x-4)(x+1)(x+4) ?

The extreme f(x)=(x-4)(x+1)(x+4) is Maximum(-8/3 , 400/27),Minimum(2,-36)

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extreme f(x)=(x-4)(x+1)(x+4)

extreme

Maximum (- \frac{8}{3}, \frac{400}{27}), Minimum (2, - 36)

Solution steps

f^{'} (x) = (x - 2) (3 x + 8)

Find intervals:

Increasing

: - \infty < x < - \frac{8}{3},

Decreasing

: - \frac{8}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - \frac{8}{3}

into

(x - 4) (x + 1) (x + 4) : \frac{400}{27}

Maximum (- \frac{8}{3}, \frac{400}{27})

Plug

x = 2

into

(x - 4) (x + 1) (x + 4) : - 36

Minimum (2, - 36)

Maximum (- \frac{8}{3}, \frac{400}{27}), Minimum (2, - 36)

What is the extreme f(x)=(x-4)(x+1)(x+4) ?
The extreme f(x)=(x-4)(x+1)(x+4) is Maximum(-8/3 , 400/27),Minimum(2,-36)