John owns a hotdog stand. he has found that his profit is represented by the equation p=-x^2+78x+89, with p being the profit in dollars, and x the number of hotdogs sold. how many hotdogs must he sell to earn the most profit?

Suppose that the price p, in dollars, and the number of sales, x, of a certain item follow the equation 4 p plus 4 x plus 2 pxequals56. suppose also that p and x are both functions of time, measured in days. find the rate at which x is changing when xequals2, pequals6, and startfraction dp over dt endfraction equals1.5.