Question

the value of c for which f(x)=x+(c/x) has a local minimum at x=3 is?

Answer 1

If x=3 is a local minimum point,
then x=3 corresponds to a critical point, ya?\[\large\rm f'(3)=0\]

Answer 2

Take derivative,
set equal to 0, (since we're looking for critical points)
Plug in x=3, (since that corresponds to a critical point)
solve for c.

Answer 3

so x+c/x is 1+c(x^-1) right then c-x^-2=0?

Answer 4

woah not sure what happened there,
looks like you took derivative of the first term twice or something.

Answer 5

and yes, the negative comes down,
but make sure you're not wring c MINUS x^-2,
that's multiplication

Answer 6

\[\large\rm x+cx^{-1}\qquad\to\qquad 1+-cx^{-2}\]

Answer 7

writing* not wring lol

Answer 8

oh okay. 1-cx^-2=0
-1/-(3^-2)=9 Thanks!

Answer 9

9? Good good good :)