TITLE: A Calculus Question, Derivatives
QUESTION [0 upvotes]: Please help and explain how to do the problem taking calc online and the teacher is not present right now

REPLY [0 votes]: The required function is an inverse linear function, which means that it has a negative gradient. You are given two points on the line, $(14, 1000)$ and $(9, 1 500)$ where $(x, y) = (dollars, pizzas)$. To find an equation for the line, you need to first find the gradient: $$m=\frac{1500-1000}{9-14}$$ Once you have done that, plug $m$ into the equation $y=mx+c$, then substitute in one of the given points to solve for c (the number of pizzas that will be sold if the price is $0.00).
Once you have the equation for the line, solve that simultaneously with the equation for revenue: $f(x)=xy$ so that you have $f(x)$ in terms of $x$. In order to maximize revenue, find where the derivative ($f'(x)$) is equal to 0.
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