Problem

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

Answer

Expert–verified
Hide Steps
Answer

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

Steps

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 $x=3$.

link_gpt

Popular Problems

Compute $\int_{0}^{\ln (2) / … Solve the triangle. \[ \mathr… QUESTION 2 - 1 POINT Solve th… 5. Suppose you are a computer… Answer the statistical measur… $(-\infty, 2) \cap(-6, \infty… A firm does not pay a dividen… Math 112 Section: 4. Tubercul… Find $y^{\prime}$ if $y=\ln \… 3. (3pts) Cherry trees in a c… More