What is the extreme f(x)=9x^2+2x^3 ?

The extreme f(x)=9x^2+2x^3 is Maximum(-3,27),Minimum(0,0)

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extreme f(x)=9x^2+2x^3

extreme points

f (x) = 9 x^{2} + 2 x^{3}

Maximum (- 3, 27), Minimum (0, 0)

Solution steps

f^{'} (x) = 18 x + 6 x^{2}

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

9 x^{2} + 2 x^{3} : 27

Maximum (- 3, 27)

Plug

x = 0

into

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

Minimum (0, 0)

Maximum (- 3, 27), Minimum (0, 0)

f (x) = \frac{4 x ^{4}}{2 x ^{2} - 3}

\frac{12 x ^{4} + 10 x - 3}{3 x ^{4}}

\frac{1}{2} (3 x - 1)

f (x) = \frac{x + 9}{x ^{2} - 81}

f (x) = \frac{x + 9}{x ^{2} - 18 x + 81}

What is the extreme f(x)=9x^2+2x^3 ?
The extreme f(x)=9x^2+2x^3 is Maximum(-3,27),Minimum(0,0)