What is the extreme f(x)=x^5-10x^4+2=x^4(x-10)+2 ?

The extreme f(x)=x^5-10x^4+2=x^4(x-10)+2 is Maximum(0,2),Minimum(8,-8190)

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extreme f(x)=x^5-10x^4+2=x^4(x-10)+2

extreme

Maximum (0, 2), Minimum (8, - 8190)

Solution steps

f^{'} (x) = 5 x^{3} (x - 8)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = 0

into

x^{4} (x - 10) + 2 : 2

Maximum (0, 2)

Plug

x = 8

into

x^{4} (x - 10) + 2 : - 8190

Minimum (8, - 8190)

Maximum (0, 2), Minimum (8, - 8190)

What is the extreme f(x)=x^5-10x^4+2=x^4(x-10)+2 ?
The extreme f(x)=x^5-10x^4+2=x^4(x-10)+2 is Maximum(0,2),Minimum(8,-8190)