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Popular >

extreme-x^3+3x^2+9

Solution

extreme points

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

Solution

Minimum (0, 9), Maximum (2, 13)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = 0

into

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

Minimum (0, 9)

Plug

x = 2

into

- x^{3} + 3 x^{2} + 9 : 13

Maximum (2, 13)

Minimum (0, 9), Maximum (2, 13)

Popular Examples

extreme f(x)=x^2+y^2+6x-12y-9 extreme points

f (x) = x^{2} + y^{2} + 6 x - 12 y - 9

extreme f(x,y)=-x^2+2xy-7y^2+2x+10y+8 extreme points

f (x, y) = - x^{2} + 2 x y - 7 y^{2} + 2 x + 10 y + 8

extreme f(x)=2xe^x-4x^3 extreme points

f (x) = 2 x e^{x} - 4 x^{3}

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f (x) = (x^{2} e^{3 x})

extreme f(x)=18500(0.25-r^2)extreme points

f (x) = 18500 (0.25 - r^{2})

Frequently Asked Questions (FAQ)

What is the extreme-x^3+3x^2+9 ?
The extreme-x^3+3x^2+9 is Minimum(0,9),Maximum(2,13)