What is the extreme f(x)=-2x^4-24x^3+12 ?

The extreme f(x)=-2x^4-24x^3+12 is Maximum(-9,4386),Saddle(0,12)

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extreme f(x)=-2x^4-24x^3+12

extreme points

f (x) = - 2 x^{4} - 24 x^{3} + 12

Maximum (- 9, 4386), Saddle (0, 12)

Solution steps

f^{'} (x) = - 8 x^{3} - 72 x^{2}

Find intervals:

Increasing

: - \infty < x < - 9,

Decreasing

: - 9 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 9

into

- 2 x^{4} - 24 x^{3} + 12 : 4386

Maximum (- 9, 4386)

Plug

x = 0

into

- 2 x^{4} - 24 x^{3} + 12 : 12

Saddle (0, 12)

Maximum (- 9, 4386), Saddle (0, 12)

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

f (x, y) = - \frac{1}{4} x^{4} + \frac{2}{3} x^{3} + 4 x y - y^{2}

f (x, y) = x y (10 - 2 x - 3 y)

P (b, s) = b + 2 s

f (x) = 2 x e^{- x}

What is the extreme f(x)=-2x^4-24x^3+12 ?
The extreme f(x)=-2x^4-24x^3+12 is Maximum(-9,4386),Saddle(0,12)