What is the extreme f(x)=x^5-5x^4+8 ?

The extreme f(x)=x^5-5x^4+8 is Maximum(0,8),Minimum(4,-248)

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extreme f(x)=x^5-5x^4+8

extreme points

f (x) = x^{5} - 5 x^{4} + 8

Maximum (0, 8), Minimum (4, - 248)

Solution steps

f^{'} (x) = 5 x^{4} - 20 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

x^{5} - 5 x^{4} + 8 : 8

Maximum (0, 8)

Plug

x = 4

into

x^{5} - 5 x^{4} + 8 : - 248

Minimum (4, - 248)

Maximum (0, 8), Minimum (4, - 248)

What is the extreme f(x)=x^5-5x^4+8 ?
The extreme f(x)=x^5-5x^4+8 is Maximum(0,8),Minimum(4,-248)