What is the extreme f(x)=20+8x^3-x^4 ?

The extreme f(x)=20+8x^3-x^4 is Saddle(0,20),Maximum(6,452)

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extreme f(x)=20+8x^3-x^4

extreme

Saddle (0, 20), Maximum (6, 452)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 6,

Decreasing

: 6 < x < \infty

Plug

x = 0

into

20 + 8 x^{3} - x^{4} : 20

Saddle (0, 20)

Plug

x = 6

into

20 + 8 x^{3} - x^{4} : 452

Maximum (6, 452)

Saddle (0, 20), Maximum (6, 452)

What is the extreme f(x)=20+8x^3-x^4 ?
The extreme f(x)=20+8x^3-x^4 is Saddle(0,20),Maximum(6,452)