E(38) = Description includes the rest of the question

Question

For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inelastic at the indicated price. (Round your answer to three decimal places.)

p = 164 − x²; p = 38

E(38) =  

Answer 1

p = 164 - x²; x = (164 - p)^1/2;

Elasticity of demand E(p) = -pf'(p)/f(p); f'(p) = - (164 - p)^-1/2/2;.

So, E(p) = p(164 - p)^-1/2/[2(164 - p)^1/2] = p/[2(164 - p)]; E(38) = 38/[2(164 - 38)] = 19/126 = .151 < 1

Demand is inelastic