What is the extreme f(x)=-20x^5-5x^4+x^2-17 ?

The extreme f(x)=-20x^5-5x^4+x^2-17 is Minimum(0,-17),Maximum(0.21858…,-16.97361…)

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extreme f(x)=-20x^5-5x^4+x^2-17

extreme points

f (x) = - 20 x^{5} - 5 x^{4} + x^{2} - 17

Minimum (0, - 17), Maximum (0.21858 \dots, - 16.97361 \dots)

Solution steps

Find the critical points:

x = 0, x \approx 0.21858 \dots

Domain of

- 20 x^{5} - 5 x^{4} + x^{2} - 17 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 0.21858 \dots,

Decreasing

: 0.21858 \dots < x < \infty

Plug the extreme point

x = 0

into

- 20 x^{5} - 5 x^{4} + x^{2} - 17 \Rightarrow y = - 17

Minimum (0, - 17)

Plug the extreme point

x = 0.21858 \dots

into

- 20 x^{5} - 5 x^{4} + x^{2} - 17 \Rightarrow y = - 16.97361 \dots

Maximum (0.21858 \dots, - 16.97361 \dots)

Minimum (0, - 17), Maximum (0.21858 \dots, - 16.97361 \dots)

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 8, - 2 \leq x \leq 4

f (x) = 2 x^{3} - 3 x^{2} - 12 + 1, - 2 \leq x \leq 3

2 x^{2} - 2 (x - 5)

Q (x, y) = x^{2} + y^{2}

- 2 x^{2} + 4 x

What is the extreme f(x)=-20x^5-5x^4+x^2-17 ?
The extreme f(x)=-20x^5-5x^4+x^2-17 is Minimum(0,-17),Maximum(0.21858…,-16.97361…)