You have to multiply by Q to get total revenue – P×Q – because marginal revenue is the derivative with respect to quantity of total revenue (it’s a calculus thing).

The −8 comes from differentiating 3,200Q − 4Q² with respect to Q (it’s that same calculus thing). I could give you a tutorial on differential calculus, but you’re probably better off just taking my word for it: they’re correct that the slope is 3,200 − 8Q.

I see. They differentiated it using calculus. Why and when is that used? Is that only use for finding the slope of marginal revenue curve? I don’t remember seeing differentiation being used anywhere through my readings

Differential calculus is used to find slopes – rates of change – in all sorts of financial applications, calculating, for example:

marginal cost

marginal revenue

marginal revenue product

modified duration

GDP growth rate

option delta

marginal rate of substitution

maximum profit

minimum total cost

minimum WACC

Integral calculus – integration is the inverse operation of differentiation – is used to find areas, and has financial applications in calculating, for example:

For a straight line, the coefficient on x (the variable on the horizontal axis) is the slope. For a curve, you have to use calculus to get the slope at a particular point, as the slope changes from point to point.

I was having an issue understanding this concept too, apologies if I’m missing something here. Once the demand function is inverted to get a slope of -4, is it correct to say that doubling this number solves for the slope of marginal revenue since MR is the revenue from selling one additional unit? I understand that differential calculus is ultimately involved but hoping to find a practical rule to apply. Thanks!