What is the extreme f(x)=6x^2-2x^3 ?

The extreme f(x)=6x^2-2x^3 is Minimum(0,0),Maximum(2,8)

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extreme f(x)=6x^2-2x^3

extreme points

f (x) = 6 x^{2} - 2 x^{3}

Minimum (0, 0), Maximum (2, 8)

Solution steps

f^{'} (x) = 12 x - 6 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

6 x^{2} - 2 x^{3} : 0

Minimum (0, 0)

Plug

x = 2

into

6 x^{2} - 2 x^{3} : 8

Maximum (2, 8)

Minimum (0, 0), Maximum (2, 8)

f (x) = \frac{x}{x ^{2} + 11 x + 28}

(0.2) (8.8)

f (x) = x - 2 + 5

y = csc (θ) (θ + cot (θ))

What is the extreme f(x)=6x^2-2x^3 ?
The extreme f(x)=6x^2-2x^3 is Minimum(0,0),Maximum(2,8)