What is the extreme f(x)=x^4-10x^2+9 ?

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

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extreme f(x)=x^4-10x^2+9

extreme points

f (x) = 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)

f (x) = x^{2} y + y^{3} - 48 y

x^{2} y - 2 x y + 3 y^{3} - 3 y

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

- x^{4} - x^{3} + x^{2} + 3 x + 2

x - ln (x)

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