What is the extreme f(x)=-3x^3+9x^2+10 ?

The extreme f(x)=-3x^3+9x^2+10 is Minimum(0,10),Maximum(2,22)

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extreme f(x)=-3x^3+9x^2+10

extreme points

f (x) = - 3 x^{3} + 9 x^{2} + 10

Minimum (0, 10), Maximum (2, 22)

Solution steps

f^{'} (x) = - 9 x^{2} + 18 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

- 3 x^{3} + 9 x^{2} + 10 : 10

Minimum (0, 10)

Plug

x = 2

into

- 3 x^{3} + 9 x^{2} + 10 : 22

Maximum (2, 22)

Minimum (0, 10), Maximum (2, 22)

f (x) = (x - y) (25 - x y)

f (x, y) = x^{2} y - 3 x y + 5 y

f (x, y) = e^{3 x^{2} + y^{2} + 6}

f (x) = x^{4} - 4 x + 7

f (x) = 400 - \frac{3600}{x + 8} - x

What is the extreme f(x)=-3x^3+9x^2+10 ?
The extreme f(x)=-3x^3+9x^2+10 is Minimum(0,10),Maximum(2,22)