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

The extreme f(x)=(x-2)(x+1)^3 is Saddle(-1,0),Minimum(5/4 ,-2187/256)

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

extreme points

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

Saddle (- 1, 0), Minimum (\frac{5}{4}, - \frac{2187}{256})

Solution steps

f^{'} (x) = (x + 1)^{2} (4 x - 5)

Find intervals:

Decreasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < \frac{5}{4},

Increasing

: \frac{5}{4} < x < \infty

Plug

x = - 1

into

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

Saddle (- 1, 0)

Plug

x = \frac{5}{4}

into

(x - 2) (x + 1)^{3} : - \frac{2187}{256}

Minimum (\frac{5}{4}, - \frac{2187}{256})

Saddle (- 1, 0), Minimum (\frac{5}{4}, - \frac{2187}{256})

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

f (x) = 6 x^{2} + 7 y^{2}

f (x) = - 5 x^{2} + 10 x + 12

14400 + 700 x + x^{2}

f (x, y) = - 8 - 6 x + 3 x^{2} + 8 y + 5 y^{2}

What is the extreme f(x)=(x-2)(x+1)^3 ?
The extreme f(x)=(x-2)(x+1)^3 is Saddle(-1,0),Minimum(5/4 ,-2187/256)