What is the extreme f(x)=(x+4)(x-1)^2 ?

The extreme f(x)=(x+4)(x-1)^2 is Maximum(-7/3 , 500/27),Minimum(1,0)

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extreme f(x)=(x+4)(x-1)^2

extreme points

f (x) = (x + 4) (x - 1)^{2}

Maximum (- \frac{7}{3}, \frac{500}{27}), Minimum (1, 0)

Solution steps

f^{'} (x) = (x - 1) (3 x + 7)

Find intervals:

Increasing

: - \infty < x < - \frac{7}{3},

Decreasing

: - \frac{7}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{7}{3}

into

(x + 4) (x - 1)^{2} : \frac{500}{27}

Maximum (- \frac{7}{3}, \frac{500}{27})

Plug

x = 1

into

(x + 4) (x - 1)^{2} : 0

Minimum (1, 0)

Maximum (- \frac{7}{3}, \frac{500}{27}), Minimum (1, 0)

f (x) = \frac{x ^{2} - 3 x}{x + 4}

y = 3 x - 5

f (x) = - 2 x + 5

f (x) = (x + 2)^{2} + 1

What is the extreme f(x)=(x+4)(x-1)^2 ?
The extreme f(x)=(x+4)(x-1)^2 is Maximum(-7/3 , 500/27),Minimum(1,0)