Using calculus to find price elastity of demand?

Question

say the demand is 4Q+96 whats the price elasticity of demand

Answer 1

price ela. is percentage change in quantity demanded due 1% change in price. thus,
p=4q+96
4q=p-96
q=p/4-24
price el=dq/dp(p/q)
=1/4(p/q)

Answer 2

the demand curve is P=4Q+96
price elasticity of demand =
{ % change in quantity / % change in price} =dQ/dP{P/Q} where dQ/dP=1/4

Answer 3

A) E(p) = (dD/dp)*(p/D) D(p)=-p^2+4 hundred dD/dp=-2p so we've E(p)=(-2p)*(p/(4 hundred-p^2)) E(p)=(-2p^2)/(4 hundred-p^2) B) E(10)=(-2*one hundred)/(4 hundred-one hundred) E(10)=-two hundred/3 hundred E(10)=-2/3=-0.66666 via certainty E(10) is between -a million and nil then the linked fee ought to be raised C) E(p)=a million (2p^2)/(4 hundred-p^2)=a million 2p^2=4 hundred-p^2 3p^2=4 hundred p^2=4 hundred/3 p=20/sqrt(3) p=11.547 so the fee will ought to be $11.55