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

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

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

extreme points

f (x) = - \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x, (- 2, 5)

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

Solution steps

Find the critical points:

x = 1, x = 3

Domain of

- \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x, (- 2, 5) : - 2 < x < 5

Find intervals:

Decreasing

: - 2 < x < 1,

Increasing

: 1 < x < 3,

Decreasing

: 3 < x < 5

Plug the extreme point

x = 1

into

- \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x \Rightarrow y = - \frac{20}{3}

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

Plug the extreme point

x = 3

into

- \frac{5 x ^{3}}{3} + 10 x^{2} - 15 x \Rightarrow y = 0

Maximum (3, 0)

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

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

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

f (x) = - x^{3} - 12 x^{2}

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

f (x) = 90 x^{2} - 0.2 x^{4}

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