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

The extreme f(x)=-x^3+15x^2 is Minimum(0,0),Maximum(10,500)

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

extreme points

f (x) = - x^{3} + 15 x^{2}

Minimum (0, 0), Maximum (10, 500)

Solution steps

f^{'} (x) = - 3 x^{2} + 30 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 10,

Decreasing

: 10 < x < \infty

Plug

x = 0

into

- x^{3} + 15 x^{2} : 0

Minimum (0, 0)

Plug

x = 10

into

- x^{3} + 15 x^{2} : 500

Maximum (10, 500)

Minimum (0, 0), Maximum (10, 500)

f (x) = \frac{x ^{2} - 14 x + 49}{x - 10}

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

(x - 8 x^{2})^{\frac{1}{3}}

f (x) = x 4 - x^{2}, - 2 \leq x \leq 2

x^{2} + 8 x + 18

What is the extreme f(x)=-x^3+15x^2 ?
The extreme f(x)=-x^3+15x^2 is Minimum(0,0),Maximum(10,500)