What is the extreme f(x)=4x^5-3x^4+x^3-2x^2+x-1 ?

The extreme f(x)=4x^5-3x^4+x^3-2x^2+x-1 is Maximum(0.27256…,-0.86630…),Minimum(0.65836…,-0.99202…)

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extreme f(x)=4x^5-3x^4+x^3-2x^2+x-1

extreme

Maximum (0.27256 \dots, - 0.86630 \dots), Minimum (0.65836 \dots, - 0.99202 \dots)

Solution steps

Find the critical points:

x \approx 0.27256 \dots, x \approx 0.65836 \dots

Domain of

4 x^{5} - 3 x^{4} + x^{3} - 2 x^{2} + x - 1 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0.27256 \dots,

Decreasing

: 0.27256 \dots < x < 0.65836 \dots,

Increasing

: 0.65836 \dots < x < \infty

Plug the extreme point

x = 0.27256 \dots

into

4 x^{5} - 3 x^{4} + x^{3} - 2 x^{2} + x - 1 \Rightarrow y = - 0.86630 \dots

Maximum (0.27256 \dots, - 0.86630 \dots)

Plug the extreme point

x = 0.65836 \dots

into

4 x^{5} - 3 x^{4} + x^{3} - 2 x^{2} + x - 1 \Rightarrow y = - 0.99202 \dots

Minimum (0.65836 \dots, - 0.99202 \dots)

Maximum (0.27256 \dots, - 0.86630 \dots), Minimum (0.65836 \dots, - 0.99202 \dots)

What is the extreme f(x)=4x^5-3x^4+x^3-2x^2+x-1 ?
The extreme f(x)=4x^5-3x^4+x^3-2x^2+x-1 is Maximum(0.27256…,-0.86630…),Minimum(0.65836…,-0.99202…)