What is the extreme f(x)=-5x^6+x^5+2x^3+4 ?

The extreme f(x)=-5x^6+x^5+2x^3+4 is Saddle(0,4),Maximum(0.64596…,4.28829…)

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extreme f(x)=-5x^6+x^5+2x^3+4

extreme points

f (x) = - 5 x^{6} + x^{5} + 2 x^{3} + 4

Saddle (0, 4), Maximum (0.64596 \dots, 4.28829 \dots)

Solution steps

Find the critical points:

x = 0, x \approx 0.64596 \dots

Domain of

- 5 x^{6} + x^{5} + 2 x^{3} + 4 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 0.64596 \dots,

Decreasing

: 0.64596 \dots < x < \infty

Plug the extreme point

x = 0

into

- 5 x^{6} + x^{5} + 2 x^{3} + 4 \Rightarrow y = 4

Saddle (0, 4)

Plug the extreme point

x = 0.64596 \dots

into

- 5 x^{6} + x^{5} + 2 x^{3} + 4 \Rightarrow y = 4.28829 \dots

Maximum (0.64596 \dots, 4.28829 \dots)

Saddle (0, 4), Maximum (0.64596 \dots, 4.28829 \dots)

What is the extreme f(x)=-5x^6+x^5+2x^3+4 ?
The extreme f(x)=-5x^6+x^5+2x^3+4 is Saddle(0,4),Maximum(0.64596…,4.28829…)