Critical values of (9/x)+x, extrema, intervals of incr/decr

[smileykd]

Find the critical values, the interals where f(x) is increasing, the intervals where f(x) is decreasing, and the local extrema.

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

 

[tkhunny]

Have you considered the first derivative?

 

[smileykd]

How would the +x fit in when I use the quotient rule for 9/x?

 

[galactus]

How would the +x fit in when I use the quotient rule for 9/x?

For heaven's sake, he means for 9/x. You know the derivative of x is 1?.

You could even use the product rule, \(\displaystyle 9x^{-1}\)

 

[tkhunny]

One piece at a time.

If you are really bent on using the Quotient Rule ONLY, you can add the fraction.

\(\displaystyle \L\,\frac{1}{x}+x\,=\,\frac{1+x^{2}}{x}\)

It is important not to forget everything you learned in algebra.