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Popular Functions >

extreme f(x)=4x+9/x

Solution

extreme points

f (x) = 4 x + \frac{9}{x}

Solution

Maximum (- \frac{3}{2}, - 12), Minimum (\frac{3}{2}, 12)

Solution steps

f^{'} (x) = 4 - \frac{9}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{3}{2},

Decreasing

: - \frac{3}{2} < x < 0,

Decreasing

: 0 < x < \frac{3}{2},

Increasing

: \frac{3}{2} < x < \infty

Plug

x = - \frac{3}{2}

into

4 x + \frac{9}{x} : - 12

Maximum (- \frac{3}{2}, - 12)

Plug

x = \frac{3}{2}

into

4 x + \frac{9}{x} : 12

Minimum (\frac{3}{2}, 12)

Maximum (- \frac{3}{2}, - 12), Minimum (\frac{3}{2}, 12)

Graph

Popular Examples

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extreme f(x)=|sin(x)|,(-pi,pi)

extreme f(x)=(x^2-63)/(x-8)

extreme f(x)=x^2+y^4+2xy

Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x+9/x ?
The extreme f(x)=4x+9/x is Maximum(-3/2 ,-12),Minimum(3/2 ,12)