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Problem:

What value of $a$ makes $$f(x)=x^2 + \frac {a}{x}$$ have (a) a minimum at $x=2$, (b) an inflection point at $x=1$?

(a) and (b) are separate and not dependent upon each other.

What I have done:

Not much. I wrote the derivative to try and find where $x=0$, but that is where I got stuck.

$$0=2x-ax^{-2} .$$

I'm not really sure what to do.

3 Answers 3