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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

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

Decreasing

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

Plug

x = 0

into

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

Minimum (0, 0)

Plug

x = \frac{10}{9}

into

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

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

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

f (x) = t 4 - t

x^{2} + \frac{1}{x}

f (x) = x^{3} - x^{2} - x + 8, - 1 \leq x \leq 0

f (x) = \frac{12 x}{9 + x ^{2}}

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

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