Hi Sonia! We use the exponential differentiation rule and the chain rule to obtain the expression for dy/dx.

At the stationary point(s) if any, dy/dx = 0 so we set the expression for dy/dx to 0 and solve it. Note that e^any real number > 0 and therefore cannot be equated to zero.

Substitute our found value(s) of x to obtain the coordinates of the stationary point(s).

We can use the first derivative test or he second derivative test to obtain the nature of the stationary point(s).

For first derivative test, we consider the signage of the value of dy/dx just before the stationary point(s) and just after the stationary point (s).

For second derivative test, we obtain d2y/dx2 and substitute in our found value(s) of x. If d2y/dx2 > 0, the stationary point is a minimum; if d2y/dx2 < 0, the stationary point is a maximum; if d2y/dx2 = 0, the result is inconclusive and we will need to rely on the first derivative test.