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

The extreme f(x)=-2x^2(x+4)(x-4) is Maximum(-2sqrt(2),128),Minimum(0,0),Maximum(2sqrt(2),128)

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

extreme points

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

Maximum (- 22, 128), Minimum (0, 0), Maximum (22, 128)

Solution steps

f^{'} (x) = - 2 (4 x^{3} - 32 x)

Find intervals:

Increasing

: - \infty < x < - 22,

Decreasing

: - 22 < x < 0,

Increasing

: 0 < x < 22,

Decreasing

: 22 < x < \infty

Plug

x = - 22

into

- 2 x^{2} (x + 4) (x - 4) : 128

Maximum (- 22, 128)

Plug

x = 0

into

- 2 x^{2} (x + 4) (x - 4) : 0

Minimum (0, 0)

Plug

x = 22

into

- 2 x^{2} (x + 4) (x - 4) : 128

Maximum (22, 128)

Maximum (- 22, 128), Minimum (0, 0), Maximum (22, 128)

5 sin (3 x - \frac{π}{2})

\frac{x ^{3}}{x ^{2} - 9}

f (x) = 2 \cdot x + 1

f (x) = x^{2} + 16

4 x - 1 + 5

What is the extreme f(x)=-2x^2(x+4)(x-4) ?
The extreme f(x)=-2x^2(x+4)(x-4) is Maximum(-2sqrt(2),128),Minimum(0,0),Maximum(2sqrt(2),128)