Mathematics

A critical point occurs where the derivative equals zero—that's where the function's slope flattens out. Since you're told $x=1$ is a critical point, you need to find $f'(x)$, then set $f'(1)=0$ and solve for $k$. This turns a condition about the original function into a simple linear equation in the unknown parameter.

A critical point occurs where the derivative equals zero—that's where the function's slope flattens out. Since you're told $x=1$ is a critical point, you need to find $f'(x)$, then set $f'(1)=0$ and solve for $k$. This turns a condition about the original function into a simple linear equation in the unknown parameter.