the derivative went from a negative value to a positive value on a continuous, smooth curve, it means the derivative had to hit zero at some point in that interval. when the derivative is zero, we have a stationary point
just find the x-value for A, which you can do, you know how to find the local minimum point of a function. then just plug in the x-value into g(x) to show that you get the desired result. that is, if is the x-value for the point A, show that by plugging it in
These aren't new questions, and they're on the same topic. They're the final questions in the chapter, and I posted them the same day you replied to the other q. Never mind.