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

The extreme f(x)=-x^4+4x^3+8x^2 is Maximum(-1,3),Minimum(0,0),Maximum(4,128)

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

extreme points

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

Maximum (- 1, 3), Minimum (0, 0), Maximum (4, 128)

Solution steps

f^{'} (x) = - 4 x^{3} + 12 x^{2} + 16 x

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 1

into

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

Maximum (- 1, 3)

Plug

x = 0

into

- x^{4} + 4 x^{3} + 8 x^{2} : 0

Minimum (0, 0)

Plug

x = 4

into

- x^{4} + 4 x^{3} + 8 x^{2} : 128

Maximum (4, 128)

Maximum (- 1, 3), Minimum (0, 0), Maximum (4, 128)

What is the extreme f(x)=-x^4+4x^3+8x^2 ?
The extreme f(x)=-x^4+4x^3+8x^2 is Maximum(-1,3),Minimum(0,0),Maximum(4,128)