Question

f(x)=ln(x)/7sqrt(x)

Find the interval on which f is increasing.
Find the interval on which f is decreasing.
Find the local maximum value of f.
Find the inflection point.
Find the interval on which f is concave up.
Find the interval on which f ins concave down.

Please and thank you!

@Mathematics

Answer 1

That is;

\[f(x)=\ln(x)/(7\sqrt{x})\]

the square root x and 7 are BOTH under the ln(x)

Answer 2

\[f(x)=\ln(\frac{x}{7 \sqrt{x}})\] like this?

Answer 3

hints to you find f'(x) then f''(x)

Answer 4

or do you mean what you actually typed which was
\[f(x)=\frac{\ln(x)}{7 \sqrt{x}}\]

Answer 5

increasing when f'(x) >0

Answer 6

decreasing when f'(x)<0

Answer 7

max when deriv = 0

Answer 8

infl when f"(x) = 0
concave up when f"(x) >0
and down when f"(x)<0

Answer 9

an interval is (#,#)... as in (-infinity,0), not just f(x)<0

Answer 10

Everything you told me I know. The hard part is finding, for concave up for instance, where f''(x)>0...... so this doesn't help at all..

Answer 11

anybody

Answer 12

Do you know how to find the derivative of the function you gave?