Question

Find the value of k for which the graph of (x^2+k/x)+x^2 has a point of inflection at x=-2.

Answer 1

\[\frac{x^2+k}{x}+x^2 \]

Answer 2

first derivative
\[1 - \frac{k}{x^2} + 2 x\]
second derivative
\[2 + \frac{2 k}{x^3}\] replace x by -2, set the result = 0, solve for k