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

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

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

extreme points

f (x) = - \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)

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

f (x) = \frac{( x ^{2} - x + 4 )}{( x + 1 )}

f (x) = 5 sin^{2} (x)

f (x) = 36 + 3 x^{2} - 2 x^{3}

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

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