Question

pressed by the following equation: dR/dt=A*dp/dt,
where A is a function of just q.

A = ?

Find dR/dt when q=15 and dp/dt=5.
dR/dt = The price (in dollars) p and the quantity demanded q are related by the equation: p^2+2q^2=1100.If R is revenue, dR/dt can be expressed by the following equation: dR/dt=A*dp/dt,
where A is a function of just q.

A = ?

Find dR/dt when q=15 and dp/dt=5.
dR/dt =

Answer 1

FOR THE FIRST PROBLEM:

Differentiating p^2 + 2q^2 = 1100 with respect to time => 2p(dp/dt) + 4q(dq/dt) = 0 

dp/dt = -2q/p(dq/dt) 

R = pq 

dR/dt = p(dq/dt) + q(dp/dt) = -p²/2q(dp/dt) + q(dp/dt) = (2q² - 1100)/2q * (dp/dt) + q(dp/dt) 

A = (2q - 550/q)

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