Problem

8. Find the value of the constant $b$ such that the following function has a point of inflection at $x=3$. $f(x)=\sqrt{x+1}+\frac{b}{x}$

Solution

Step 1 :Find the second derivative of the function $f(x) = \sqrt{x+1} + \frac{b}{x}$.

Step 2 :Calculate the second derivative at $x=3$ and set it equal to 0.

Step 3 :Solve the equation $\frac{2b}{27} - \frac{1}{32} = 0$ for the value of $b$.

Step 4 :\(\boxed{\frac{27}{64}}\) is the value of the constant $b$ such that the function has a point of inflection at $x=3$.

From Solvely APP
Source: https://solvelyapp.com/problems/8070/

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