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 points

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

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)

f (x) = - x^{2} + 12 x + 80

f (x) = x \cdot (4 - 2 x) \cdot (11 - 2 x)

x^{3} + y^{3} - 3 x^{2} - 9 y^{2} - 9 x

f (x, y) = 2 x y - x^{2} - 6 y^{2} + 4 x + 1

f (x) = - x^{2} - 2 x + 99

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)