Finding the Constant to Achieve a Point of Inflection

Question

The function f(x) = (x+1)^0.5 + b/x needs a point of inflection at x = 3. I'm looking for a value of b that will give me a point of inflection at x=3. I'm not sure how to do that, could someone help me figure this out?

Answer 1

Here are a few check points in the process:

$f'(x)=\frac{1}{2}(x+1)^\frac{-1}{2}-bx^{-2}$

$f''(x)=\frac{-1}{4}(x+1)^\frac{-3}{2}+2bx^{-3}$

Now you need to solve $f''(3)=0$ for $b$ So your equation should look like:

$f''(3)=0 $

$\frac{-1}{4}(3+1)^{\frac{-3}{2}}+2b(3)^{-3}=0$