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}

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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.

Answer

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.

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

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8. Find the value of the constant b such that the following function has a point of inflection at x=3. f(x)=x+1+bx

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Popular Problems

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