Prove that the marginal cost function intersects the average cost function at the point...

Prove that the marginal cost function intersects the average cost function at the point where the average cost is minimized (as shown in the following diagram) by justifying each numbered step ?–? in the following series of equations.

At the x-value where the average cost function

? Finally, explain why the equality of the first and last expressions in the series of equations proves the result.