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

The extreme y=(x-1)^2(x+1) is Maximum(-1/3 , 32/27),Minimum(1,0)

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extreme y=(x-1)^2(x+1)

extreme points

y = (x - 1)^{2} (x + 1)

Maximum (- \frac{1}{3}, \frac{32}{27}), Minimum (1, 0)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

: 1 < x < \infty

Plug

x = - \frac{1}{3}

into

(x - 1)^{2} (x + 1) : \frac{32}{27}

Maximum (- \frac{1}{3}, \frac{32}{27})

Plug

x = 1

into

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

Minimum (1, 0)

Maximum (- \frac{1}{3}, \frac{32}{27}), Minimum (1, 0)

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

f (x) = 5 x^{2} - 20 x + 5, 0 \leq x \leq 3

f (x) = x^{\frac{2}{3}} (\frac{1}{8} x^{2} + \frac{3}{5} x - 9)

f (x) = 5 - 8 x, x \geq 1

f (x, y) = 6 x^{2} - x y + 4 y^{2}

What is the extreme y=(x-1)^2(x+1) ?
The extreme y=(x-1)^2(x+1) is Maximum(-1/3 , 32/27),Minimum(1,0)