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

The extreme f(x)=x^5-5x^4+5=x^4(x-5)+5 is Maximum(0,5),Minimum(4,-251)

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

extreme

Maximum (0, 5), Minimum (4, - 251)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

x^{4} (x - 5) + 5 : 5

Maximum (0, 5)

Plug

x = 4

into

x^{4} (x - 5) + 5 : - 251

Minimum (4, - 251)

Maximum (0, 5), Minimum (4, - 251)

What is the extreme f(x)=x^5-5x^4+5=x^4(x-5)+5 ?
The extreme f(x)=x^5-5x^4+5=x^4(x-5)+5 is Maximum(0,5),Minimum(4,-251)