What is the extreme f(x)=(x-1)^2(x+3) ?

The extreme f(x)=(x-1)^2(x+3) is Maximum(-5/3 , 256/27),Minimum(1,0)

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extreme f(x)=(x-1)^2(x+3)

extreme points

f (x) = (x - 1)^{2} (x + 3)

Maximum (- \frac{5}{3}, \frac{256}{27}), Minimum (1, 0)

Solution steps

f^{'} (x) = (x - 1) (3 x + 5)

Find intervals:

Increasing

: - \infty < x < - \frac{5}{3},

Decreasing

: - \frac{5}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - \frac{5}{3}

into

(x - 1)^{2} (x + 3) : \frac{256}{27}

Maximum (- \frac{5}{3}, \frac{256}{27})

Plug

x = 1

into

(x - 1)^{2} (x + 3) : 0

Minimum (1, 0)

Maximum (- \frac{5}{3}, \frac{256}{27}), Minimum (1, 0)

What is the extreme f(x)=(x-1)^2(x+3) ?
The extreme f(x)=(x-1)^2(x+3) is Maximum(-5/3 , 256/27),Minimum(1,0)