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Popular >

extreme f(x)=x+9/x+2

Solution

extreme points

f (x) = x + \frac{9}{x} + 2

Solution

Maximum (- 3, - 4), Minimum (3, 8)

Solution steps

f^{'} (x) = - \frac{9}{x ^{2}} + 1

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

x + \frac{9}{x} + 2 : - 4

Maximum (- 3, - 4)

Plug

x = 3

into

x + \frac{9}{x} + 2 : 8

Minimum (3, 8)

Maximum (- 3, - 4), Minimum (3, 8)

Popular Examples

extreme f(x,y)=x^3+y^3-3x-12y+30 extreme points

f (x, y) = x^{3} + y^{3} - 3 x - 12 y + 30

extreme f(x,y)=-3x^2+2y^2 extreme points

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

extreme+2.5t^2+6t extreme points

+ 2.5 t^{2} + 6 t

extreme f(x)=8x^3-6x^2 extreme points

f (x) = 8 x^{3} - 6 x^{2}

extreme f(x)=e^{-2x^2}-3y^2+2y extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x+9/x+2 ?
The extreme f(x)=x+9/x+2 is Maximum(-3,-4),Minimum(3,8)