What is the extreme f(x)=-5x^3+25x^2+15 ?

The extreme f(x)=-5x^3+25x^2+15 is Minimum(0,15),Maximum(10/3 , 2905/27)

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extreme f(x)=-5x^3+25x^2+15

extreme

Minimum (0, 15), Maximum (\frac{10}{3}, \frac{2905}{27})

Solution steps

f^{'} (x) = - 15 x^{2} + 50 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{10}{3},

Decreasing

: \frac{10}{3} < x < \infty

Plug

x = 0

into

- 5 x^{3} + 25 x^{2} + 15 : 15

Minimum (0, 15)

Plug

x = \frac{10}{3}

into

- 5 x^{3} + 25 x^{2} + 15 : \frac{2905}{27}

Maximum (\frac{10}{3}, \frac{2905}{27})

Minimum (0, 15), Maximum (\frac{10}{3}, \frac{2905}{27})

What is the extreme f(x)=-5x^3+25x^2+15 ?
The extreme f(x)=-5x^3+25x^2+15 is Minimum(0,15),Maximum(10/3 , 2905/27)