What is the extreme f(x)=-(5x^3)/3+10x^2+25x ?

The extreme f(x)=-(5x^3)/3+10x^2+25x is Minimum(-1,-40/3),Maximum(5, 500/3)

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extreme f(x)=-(5x^3)/3+10x^2+25x

extreme

Minimum (- 1, - \frac{40}{3}), Maximum (5, \frac{500}{3})

Solution steps

f^{'} (x) = - 5 x^{2} + 20 x + 25

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 5,

Decreasing

: 5 < x < \infty

Plug

x = - 1

into

- \frac{5 x ^{3}}{3} + 10 x^{2} + 25 x : - \frac{40}{3}

Minimum (- 1, - \frac{40}{3})

Plug

x = 5

into

- \frac{5 x ^{3}}{3} + 10 x^{2} + 25 x : \frac{500}{3}

Maximum (5, \frac{500}{3})

Minimum (- 1, - \frac{40}{3}), Maximum (5, \frac{500}{3})

What is the extreme f(x)=-(5x^3)/3+10x^2+25x ?
The extreme f(x)=-(5x^3)/3+10x^2+25x is Minimum(-1,-40/3),Maximum(5, 500/3)