What is the extreme f(x)=x^4+6x^5-x ?

The extreme f(x)=x^4+6x^5-x is Maximum(-0.46495…,0.38131…),Minimum(0.39747…,-0.31299…)

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extreme f(x)=x^4+6x^5-x

extreme points

f (x) = x^{4} + 6 x^{5} - x

Maximum (- 0.46495 \dots, 0.38131 \dots), Minimum (0.39747 \dots, - 0.31299 \dots)

Solution steps

Find the critical points:

x \approx - 0.46495 \dots, x \approx 0.39747 \dots

Domain of

x^{4} + 6 x^{5} - x : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - 0.46495 \dots,

Decreasing

: - 0.46495 \dots < x < 0.39747 \dots,

Increasing

: 0.39747 \dots < x < \infty

Plug the extreme point

x = - 0.46495 \dots

into

x^{4} + 6 x^{5} - x \Rightarrow y = 0.38131 \dots

Maximum (- 0.46495 \dots, 0.38131 \dots)

Plug the extreme point

x = 0.39747 \dots

into

x^{4} + 6 x^{5} - x \Rightarrow y = - 0.31299 \dots

Minimum (0.39747 \dots, - 0.31299 \dots)

Maximum (- 0.46495 \dots, 0.38131 \dots), Minimum (0.39747 \dots, - 0.31299 \dots)

What is the extreme f(x)=x^4+6x^5-x ?
The extreme f(x)=x^4+6x^5-x is Maximum(-0.46495…,0.38131…),Minimum(0.39747…,-0.31299…)