What is the extreme f(x)=-2x^3+6x^2-5 ?

The extreme f(x)=-2x^3+6x^2-5 is Minimum(0,-5),Maximum(2,3)

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extreme f(x)=-2x^3+6x^2-5

extreme points

f (x) = - 2 x^{3} + 6 x^{2} - 5

Minimum (0, - 5), Maximum (2, 3)

Solution steps

f^{'} (x) = - 6 x^{2} + 12 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

- 2 x^{3} + 6 x^{2} - 5 : - 5

Minimum (0, - 5)

Plug

x = 2

into

- 2 x^{3} + 6 x^{2} - 5 : 3

Maximum (2, 3)

Minimum (0, - 5), Maximum (2, 3)

x^{4} - 8 x^{3} + 16 x^{2}

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

f (x, y) = 2 x^{2} - 8 x + y^{2} - 8 y + 6

f (x) = x e^{- 4 x}, 0 \leq x \leq 2

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

What is the extreme f(x)=-2x^3+6x^2-5 ?
The extreme f(x)=-2x^3+6x^2-5 is Minimum(0,-5),Maximum(2,3)