What is the extreme f(x)=(x^2+10)(100-x^2) ?

The extreme f(x)=(x^2+10)(100-x^2) is Maximum(-3sqrt(5),3025),Minimum(0,1000),Maximum(3sqrt(5),3025)

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extreme f(x)=(x^2+10)(100-x^2)

extreme

Maximum (- 35, 3025), Minimum (0, 1000), Maximum (35, 3025)

Solution steps

f^{'} (x) = - 4 x (x + 35) (x - 35)

Find intervals:

Increasing

: - \infty < x < - 35,

Decreasing

: - 35 < x < 0,

Increasing

: 0 < x < 35,

Decreasing

: 35 < x < \infty

Plug

x = - 35

into

(x^{2} + 10) (100 - x^{2}) : 3025

Maximum (- 35, 3025)

Plug

x = 0

into

(x^{2} + 10) (100 - x^{2}) : 1000

Minimum (0, 1000)

Plug

x = 35

into

(x^{2} + 10) (100 - x^{2}) : 3025

Maximum (35, 3025)

Maximum (- 35, 3025), Minimum (0, 1000), Maximum (35, 3025)

What is the extreme f(x)=(x^2+10)(100-x^2) ?
The extreme f(x)=(x^2+10)(100-x^2) is Maximum(-3sqrt(5),3025),Minimum(0,1000),Maximum(3sqrt(5),3025)