What is the extreme f(x)=4x^7+9x^5-3x^4+2x^2-5 ?

The extreme f(x)=4x^7+9x^5-3x^4+2x^2-5 is Maximum(-0.36608…,-4.84854…),Minimum(0,-5)

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extreme f(x)=4x^7+9x^5-3x^4+2x^2-5

extreme points

f (x) = 4 x^{7} + 9 x^{5} - 3 x^{4} + 2 x^{2} - 5

Maximum (- 0.36608 \dots, - 4.84854 \dots), Minimum (0, - 5)

Solution steps

Find the critical points:

x \approx - 0.36608 \dots, x = 0

Domain of

4 x^{7} + 9 x^{5} - 3 x^{4} + 2 x^{2} - 5 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - 0.36608 \dots,

Decreasing

: - 0.36608 \dots < x < 0,

Increasing

: 0 < x < \infty

Plug the extreme point

x = - 0.36608 \dots

into

4 x^{7} + 9 x^{5} - 3 x^{4} + 2 x^{2} - 5 \Rightarrow y = - 4.84854 \dots

Maximum (- 0.36608 \dots, - 4.84854 \dots)

Plug the extreme point

x = 0

into

4 x^{7} + 9 x^{5} - 3 x^{4} + 2 x^{2} - 5 \Rightarrow y = - 5

Minimum (0, - 5)

Maximum (- 0.36608 \dots, - 4.84854 \dots), Minimum (0, - 5)

f (x, y) = x^{2} + y - e^{x + y}

f (x) = x^{3} + y^{2} - 6 x^{2} + y - 1

- x

f (x) = \frac{3 x}{x + 2}

f (x) = 6 x + 4 y + 2 z = 24

What is the extreme f(x)=4x^7+9x^5-3x^4+2x^2-5 ?
The extreme f(x)=4x^7+9x^5-3x^4+2x^2-5 is Maximum(-0.36608…,-4.84854…),Minimum(0,-5)