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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

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

Maximum (- 2, 8)

Plug

x = 0

into

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

Minimum (0, 0)

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

(0.3, 0.7), (0.1, 0.9)

f (x) = \frac{2 x + 4}{x ^{2} - 5 x}

f (x) = 4 - 5 x + x^{2}

\frac{1}{x} - 4

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

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