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Popular >

extreme f(x)= x/(ln(9x))

Solution

extreme points

f (x) = \frac{x}{ln ( 9 x )}

Solution

Minimum (\frac{e}{9}, \frac{e}{9})

Solution steps

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

Find intervals:

Decreasing

: 0 < x < \frac{1}{9},

Decreasing

: \frac{1}{9} < x < \frac{e}{9},

Increasing

: \frac{e}{9} < x < \infty

Plug

x = \frac{e}{9}

into

\frac{x}{ln ( 9 x )} : \frac{e}{9}

Minimum (\frac{e}{9}, \frac{e}{9})

Popular Examples

extreme 1x^3-4x^2-3x+30 extreme points

1 x^{3} - 4 x^{2} - 3 x + 30

extreme f(x)=-4x^3-6x^2+144x-11 extreme points

f (x) = - 4 x^{3} - 6 x^{2} + 144 x - 11

extreme f(x)=3x^{4/3}-2x extreme points

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

extreme y=4sqrt(3)x+8cos(x),0<= x<= 2pi extreme points

y = 43 x + 8 cos (x), 0 \leq x \leq 2 π

extreme f(x)=x^3-6x^2-63x+7,-4<= x<= 8 extreme points

f (x) = x^{3} - 6 x^{2} - 63 x + 7, - 4 \leq x \leq 8

Frequently Asked Questions (FAQ)

What is the extreme f(x)= x/(ln(9x)) ?
The extreme f(x)= x/(ln(9x)) is Minimum(e/9 , e/9)