What is the extreme f(x)=-2x^3+12x^2+18 ?

The extreme f(x)=-2x^3+12x^2+18 is Minimum(0,18),Maximum(4,82)

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extreme f(x)=-2x^3+12x^2+18

extreme points

f (x) = - 2 x^{3} + 12 x^{2} + 18

Minimum (0, 18), Maximum (4, 82)

Solution steps

f^{'} (x) = - 6 x^{2} + 24 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

- 2 x^{3} + 12 x^{2} + 18 : 18

Minimum (0, 18)

Plug

x = 4

into

- 2 x^{3} + 12 x^{2} + 18 : 82

Maximum (4, 82)

Minimum (0, 18), Maximum (4, 82)

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

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

f (x, y) = 2 x y - 5 x^{2} - 2 y^{2} + 18 y - 8

f (x) = (x + 1)^{\frac{2}{3}} (x - 3)^{2}

f (x) = \frac{1}{4} x^{4} + \frac{4}{3} x^{3} + 2 x^{2}

What is the extreme f(x)=-2x^3+12x^2+18 ?
The extreme f(x)=-2x^3+12x^2+18 is Minimum(0,18),Maximum(4,82)