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

The extreme f(x)=5x^4-x^5+5 is Minimum(0,5),Maximum(4,261)

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

extreme points

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

Minimum (0, 5), Maximum (4, 261)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

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

Minimum (0, 5)

Plug

x = 4

into

5 x^{4} - x^{5} + 5 : 261

Maximum (4, 261)

Minimum (0, 5), Maximum (4, 261)

f (x) = 2 x + 4 sin (x)

f (x) = x^{2} - 6 x - 8

f (x) = 6 x^{2} - 6

24 x^{3} - 24 x^{2}

f (x) = 4 x^{3} - 16

What is the extreme f(x)=5x^4-x^5+5 ?
The extreme f(x)=5x^4-x^5+5 is Minimum(0,5),Maximum(4,261)