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Popular >

extreme (x^2+9)/(2x)

Solution

extreme points

\frac{x ^{2} + 9}{2 x}

Solution

Maximum (- 3, - 3), Minimum (3, 3)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

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

Maximum (- 3, - 3)

Plug

x = 3

into

\frac{x ^{2} + 9}{2 x} : 3

Minimum (3, 3)

Maximum (- 3, - 3), Minimum (3, 3)

Popular Examples

extreme f(x)=x^4-8x^2+16[-1.4]extreme points

f (x) = x^{4} - 8 x^{2} + 16 [- 1.4]

extreme f(x)=3x-x^3+5 extreme points

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

extreme x^3+3x^2-16 extreme points

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

extreme f(x)=2cos(x)-sin(2x)extreme points

f (x) = 2 cos (x) - sin (2 x)

extreme+(6x^2+35x-6)/(4x^2+23x-6)extreme points

+ \frac{6 x ^{2} + 35 x - 6}{4 x ^{2} + 23 x - 6}

Frequently Asked Questions (FAQ)

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