PLLEASEE HELP :)!
The price p and the quantity x sold of a certain product obey the demand equation below.
x=-4p+80, 0≤ p≤ 20
(a)Express the revenue R as a function of x.
(b)What is the revenue if 44 units are sold?
(c)What quantity x maximizes revenue? What is the maximum revenue?
(d)What price should the company charge to maximize revenue?
(e)What price should the company charge to earn at least $364 in revenue?

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

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step-by-step explanation:

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1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.