What is the extreme f(x)=-2x^4+8x^3-30 ?

The extreme f(x)=-2x^4+8x^3-30 is Saddle(0,-30),Maximum(3,24)

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extreme f(x)=-2x^4+8x^3-30

extreme points

f (x) = - 2 x^{4} + 8 x^{3} - 30

Saddle (0, - 30), Maximum (3, 24)

Solution steps

f^{'} (x) = - 8 x^{3} + 24 x^{2}

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

- 2 x^{4} + 8 x^{3} - 30 : - 30

Saddle (0, - 30)

Plug

x = 3

into

- 2 x^{4} + 8 x^{3} - 30 : 24

Maximum (3, 24)

Saddle (0, - 30), Maximum (3, 24)

What is the extreme f(x)=-2x^4+8x^3-30 ?
The extreme f(x)=-2x^4+8x^3-30 is Saddle(0,-30),Maximum(3,24)