# Calculus

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Q #4. Acme can produce DVD players at a cost of $140 each and market analysis estimates that if the players are sold at x dollars apiece, consumers in a region will buy approximately 2000e^-0.008x machines per week. At what price should the players be sold to maximize profit?

Q #5. Find an equation of the tangent line to the graph of the relation given by

x^2 - 6xy + y^2 = -23 at the point (2, 3) .

Q #6. If 3xy - 4x^2 = 2y^2 - 5x, then y' = ?

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#### Solution Preview

Q4)

p(x) = profit = x *(2000e^-0.008x) - 140*(2000e^-0.008x)

dp(x)/dx = 2000e^-0.008x - x *(16e^-0.008x) + 2240e^-0.008x

when ...

#### Solution Summary

This solution provides an example of a maximization problem, differentiation, and equation of a tangent line.

$2.49