What is the extreme f(x)=3x^3+5x^2 ?

The extreme f(x)=3x^3+5x^2 is Maximum(-10/9 , 500/243),Minimum(0,0)

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extreme f(x)=3x^3+5x^2

extreme points

f (x) = 3 x^{3} + 5 x^{2}

Maximum (- \frac{10}{9}, \frac{500}{243}), Minimum (0, 0)

Solution steps

f^{'} (x) = 9 x^{2} + 10 x

Find intervals:

Increasing

: - \infty < x < - \frac{10}{9},

Decreasing

: - \frac{10}{9} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - \frac{10}{9}

into

3 x^{3} + 5 x^{2} : \frac{500}{243}

Maximum (- \frac{10}{9}, \frac{500}{243})

Plug

x = 0

into

3 x^{3} + 5 x^{2} : 0

Minimum (0, 0)

Maximum (- \frac{10}{9}, \frac{500}{243}), Minimum (0, 0)

f (x) = 5^{x - 3}

3 x^{2} + 5 x + 2

\frac{5 x + 9}{4 x - 5}

y = x^{3} - 5 x^{2} + 3 x + 2

f (x) = x^{2} - 8 x + 7

What is the extreme f(x)=3x^3+5x^2 ?
The extreme f(x)=3x^3+5x^2 is Maximum(-10/9 , 500/243),Minimum(0,0)