What is the extreme x^4-10x^2+9 ?

The extreme x^4-10x^2+9 is Minimum(-sqrt(5),-16),Maximum(0,9),Minimum(sqrt(5),-16)

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extreme x^4-10x^2+9

extreme points

x^{4} - 10 x^{2} + 9

Minimum (- 5, - 16), Maximum (0, 9), Minimum (5, - 16)

Solution steps

f^{'} (x) = 4 x^{3} - 20 x

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

x^{4} - 10 x^{2} + 9 : - 16

Minimum (- 5, - 16)

Plug

x = 0

into

x^{4} - 10 x^{2} + 9 : 9

Maximum (0, 9)

Plug

x = 5

into

x^{4} - 10 x^{2} + 9 : - 16

Minimum (5, - 16)

Minimum (- 5, - 16), Maximum (0, 9), Minimum (5, - 16)

P (x, y) = 3 x^{2} + 4 x y + y^{2} + 4 x + 2 y + 1

\frac{( x - 1 ) ^{2}}{x ^{2} + 1}

f (x) = x^{\frac{4}{5}} (x - 4)

\frac{x ^{2} - x}{8 x ^{2} + 1}

(5 - x)^{3}

What is the extreme x^4-10x^2+9 ?
The extreme x^4-10x^2+9 is Minimum(-sqrt(5),-16),Maximum(0,9),Minimum(sqrt(5),-16)