What is the extreme f(x)=-x^4+4x^3+20 ?

The extreme f(x)=-x^4+4x^3+20 is Saddle(0,20),Maximum(3,47)

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extreme f(x)=-x^4+4x^3+20

extreme points

f (x) = - x^{4} + 4 x^{3} + 20

Saddle (0, 20), Maximum (3, 47)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 0

into

- x^{4} + 4 x^{3} + 20 : 20

Saddle (0, 20)

Plug

x = 3

into

- x^{4} + 4 x^{3} + 20 : 47

Maximum (3, 47)

Saddle (0, 20), Maximum (3, 47)

What is the extreme f(x)=-x^4+4x^3+20 ?
The extreme f(x)=-x^4+4x^3+20 is Saddle(0,20),Maximum(3,47)