What is the extreme f(x)=4x^3+9x^2 ?

The extreme f(x)=4x^3+9x^2 is Maximum(-3/2 , 27/4),Minimum(0,0)

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extreme f(x)=4x^3+9x^2

extreme points

f (x) = 4 x^{3} + 9 x^{2}

Maximum (- \frac{3}{2}, \frac{27}{4}), Minimum (0, 0)

Solution steps

f^{'} (x) = 12 x^{2} + 18 x

Find intervals:

Increasing

: - \infty < x < - \frac{3}{2},

Decreasing

: - \frac{3}{2} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{3}{2}

into

4 x^{3} + 9 x^{2} : \frac{27}{4}

Maximum (- \frac{3}{2}, \frac{27}{4})

Plug

x = 0

into

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

Minimum (0, 0)

Maximum (- \frac{3}{2}, \frac{27}{4}), Minimum (0, 0)

f (x, y) = x^{2} \cdot y^{2} + x^{2} - x \cdot y^{2} - 5 \cdot x - 7

\frac{3 x}{x - 2}

f (x, y) = 8 x y + \frac{1}{x} + \frac{1}{y}

f (x, y) = 3 x y - 6 x - 3 y + 7

5 + 6 x - 8 x^{3}

What is the extreme f(x)=4x^3+9x^2 ?
The extreme f(x)=4x^3+9x^2 is Maximum(-3/2 , 27/4),Minimum(0,0)