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

The extreme f(x)=(1-x)^2*(1+x)^3 is Saddle(-1,0),Maximum(1/5 , 3456/3125),Minimum(1,0)

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

extreme points

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

Saddle (- 1, 0), Maximum (\frac{1}{5}, \frac{3456}{3125}), Minimum (1, 0)

Solution steps

f^{'} (x) = (1 + x)^{2} (x - 1) (5 x - 1)

Find intervals:

Increasing

: - \infty < x < - 1,

Increasing

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

Decreasing

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

Increasing

: 1 < x < \infty

Plug

x = - 1

into

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

Saddle (- 1, 0)

Plug

x = \frac{1}{5}

into

(1 - x)^{2} \cdot (1 + x)^{3} : \frac{3456}{3125}

Maximum (\frac{1}{5}, \frac{3456}{3125})

Plug

x = 1

into

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

Minimum (1, 0)

Saddle (- 1, 0), Maximum (\frac{1}{5}, \frac{3456}{3125}), Minimum (1, 0)

f (x) = \frac{x ^{4} - 5 x + 7}{x ^{2} + 1}

f (x) = 5 - 6 x^{2}

y = \frac{- 8 - 8 x ^{2}}{2 x ( 1 + x )}

f (t) = \frac{e ^{t}}{t ^{2} + 1}

\frac{x + 3}{x - 2}

What is the extreme f(x)=(1-x)^2*(1+x)^3 ?
The extreme f(x)=(1-x)^2*(1+x)^3 is Saddle(-1,0),Maximum(1/5 , 3456/3125),Minimum(1,0)