What is the extreme f(x)=(x^2-25)^2 ?

The extreme f(x)=(x^2-25)^2 is Minimum(-5,0),Maximum(0,625),Minimum(5,0)

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extreme f(x)=(x^2-25)^2

extreme points

f (x) = (x^{2} - 25)^{2}

Minimum (- 5, 0), Maximum (0, 625), Minimum (5, 0)

Solution steps

f^{'} (x) = 4 x (x^{2} - 25)

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

(x^{2} - 25)^{2} : 0

Minimum (- 5, 0)

Plug

x = 0

into

(x^{2} - 25)^{2} : 625

Maximum (0, 625)

Plug

x = 5

into

(x^{2} - 25)^{2} : 0

Minimum (5, 0)

Minimum (- 5, 0), Maximum (0, 625), Minimum (5, 0)

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

(x^{2} + 12) (144 - x^{2})

f (x) = \frac{10 x ^{3}}{3} - \frac{11 x ^{2}}{2} + x + 2

5 + 4 x^{2} - x^{4}

f (x) = x^{2} + 3, - 1 \leq x \leq 4

What is the extreme f(x)=(x^2-25)^2 ?
The extreme f(x)=(x^2-25)^2 is Minimum(-5,0),Maximum(0,625),Minimum(5,0)