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

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

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

extreme points

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

Saddle (- 2, 0), Maximum (\frac{1}{4}, \frac{2187}{256})

Solution steps

f^{'} (x) = - (x + 2)^{3} - 3 x^{3} - 9 x^{2} + 12

Find intervals:

Increasing

: - \infty < x < - 2,

Increasing

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

Decreasing

: \frac{1}{4} < x < \infty

Plug

x = - 2

into

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

Saddle (- 2, 0)

Plug

x = \frac{1}{4}

into

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

Maximum (\frac{1}{4}, \frac{2187}{256})

Saddle (- 2, 0), Maximum (\frac{1}{4}, \frac{2187}{256})

x^{4} - 4 x^{3} + 14

f (x) = \frac{2 x ^{2} + 18}{x}

f (x) = - x^{2} - 15.9 x - 57

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

f (x) = \frac{- x ^{2} - 10 x - 13}{x + 9}

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