What is the extreme f(x)=x^4-200x^2+10000 ?

The extreme f(x)=x^4-200x^2+10000 is Minimum(-10,0),Maximum(0,10000),Minimum(10,0)

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extreme f(x)=x^4-200x^2+10000

extreme points

f (x) = x^{4} - 200 x^{2} + 10000

Minimum (- 10, 0), Maximum (0, 10000), Minimum (10, 0)

Solution steps

f^{'} (x) = 4 x^{3} - 400 x

Find intervals:

Decreasing

: - \infty < x < - 10,

Increasing

: - 10 < x < 0,

Decreasing

: 0 < x < 10,

Increasing

: 10 < x < \infty

Plug

x = - 10

into

x^{4} - 200 x^{2} + 10000 : 0

Minimum (- 10, 0)

Plug

x = 0

into

x^{4} - 200 x^{2} + 10000 : 10000

Maximum (0, 10000)

Plug

x = 10

into

x^{4} - 200 x^{2} + 10000 : 0

Minimum (10, 0)

Minimum (- 10, 0), Maximum (0, 10000), Minimum (10, 0)

y = x + 6

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

f (x) = \frac{( x - 5 )}{3}

y = \frac{1}{x - 8}

f (x) = \frac{1}{x ^{2} - 2}

What is the extreme f(x)=x^4-200x^2+10000 ?
The extreme f(x)=x^4-200x^2+10000 is Minimum(-10,0),Maximum(0,10000),Minimum(10,0)