What is the extreme f(x)=-3x^4+4x^3+72x^2 ?

The extreme f(x)=-3x^4+4x^3+72x^2 is Maximum(-3,297),Minimum(0,0),Maximum(4,640)

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extreme f(x)=-3x^4+4x^3+72x^2

extreme points

f (x) = - 3 x^{4} + 4 x^{3} + 72 x^{2}

Maximum (- 3, 297), Minimum (0, 0), Maximum (4, 640)

Solution steps

f^{'} (x) = - 12 x^{3} + 12 x^{2} + 144 x

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = - 3

into

- 3 x^{4} + 4 x^{3} + 72 x^{2} : 297

Maximum (- 3, 297)

Plug

x = 0

into

- 3 x^{4} + 4 x^{3} + 72 x^{2} : 0

Minimum (0, 0)

Plug

x = 4

into

- 3 x^{4} + 4 x^{3} + 72 x^{2} : 640

Maximum (4, 640)

Maximum (- 3, 297), Minimum (0, 0), Maximum (4, 640)

f (x, y) = 16 - x^{2} - y^{2}

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

f (x) = \frac{x - 6}{x ^{2} - 16}, 0 \leq x < 4

(4 - x) 4^{x}

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

What is the extreme f(x)=-3x^4+4x^3+72x^2 ?
The extreme f(x)=-3x^4+4x^3+72x^2 is Maximum(-3,297),Minimum(0,0),Maximum(4,640)