Stationary points are where the first derivative is equal to 0.
First, find using the chain rule.
Now set equal to 0 and solve for .
Now evaluate the function when .
Therefore, the function has a stationary point at .
Finally, determine whether this point is a local minimum or a
local maximum by evaluating the second derivative at this point.
As , this does not show whether the
stationary point is a local minimum or a local maximum. Instead,
consider the slope on either side of the stationary point.
The slope changes from negative to positive, and therefore the
stationary point is a local minimum.
Hence, the function has a local minimum at the point