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

The extreme f(x)=x^5+5x^4 is Maximum(-4,256),Minimum(0,0)

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

extreme points

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

Maximum (- 4, 256), Minimum (0, 0)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 4

into

x^{5} + 5 x^{4} : 256

Maximum (- 4, 256)

Plug

x = 0

into

x^{5} + 5 x^{4} : 0

Minimum (0, 0)

Maximum (- 4, 256), Minimum (0, 0)

f (x) = 6 x + 9

f (x) = x^{3} - 7

f (x) = \frac{6 x}{x ^{2} + 9}

6 sin (\frac{π}{3} x) + 1

f (x) = 9 x - x^{2}

What is the extreme f(x)=x^5+5x^4 ?
The extreme f(x)=x^5+5x^4 is Maximum(-4,256),Minimum(0,0)