What is the extreme-(5x^3)/3+10x^2-15x ?

The extreme-(5x^3)/3+10x^2-15x is Minimum(1,-20/3),Maximum(3,0)

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extreme-(5x^3)/3+10x^2-15x

extreme points

- \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x

Minimum (1, - \frac{20}{3}), Maximum (3, 0)

Solution steps

f^{'} (x) = - 5 x^{2} + 20 x - 15

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = 1

into

- \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x : - \frac{20}{3}

Minimum (1, - \frac{20}{3})

Plug

x = 3

into

- \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x : 0

Maximum (3, 0)

Minimum (1, - \frac{20}{3}), Maximum (3, 0)

\frac{x}{( x + 2 ) ^{2}}

f (x) = (1 - 2 x)^{3}

f (x) = 3 x + 5

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

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

What is the extreme-(5x^3)/3+10x^2-15x ?
The extreme-(5x^3)/3+10x^2-15x is Minimum(1,-20/3),Maximum(3,0)