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

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

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

extreme points

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

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

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} + 5 : 5

Maximum (0, 5)

Plug

x = 4

into

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

Minimum (4, - 251)

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

f (x) = x^{2} + y^{2} + 8 x - 12 y - 7

4 x^{3} - 48 x - 6

f (x) = \frac{1}{4} x^{4} - 4 x^{2} + 2

300 x - 4 x^{3}

x^{3} + 12 x^{2} - 27 x + 2

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