Managerial Economics

Question

Differentiate the following

a. the profit function 𝜋 = – 2𝑄3 + 15𝑄2 − 24𝑄 − 3

b. the total revenue function 𝑇𝑅 = 50𝑄 − 3𝑄2

c. the function 𝑥2 (𝑥2 + 2𝑥 − 5 )

Answer 1

a. The derivative of the profit function 𝜋 = –2𝑄3 + 15𝑄2 − 24𝑄 − 3 is:

𝜋' = -6𝑄^2 + 30𝑄 - 24

b. The derivative of the total revenue function 𝑇𝑅 = 50𝑄 − 3𝑄^2 is:

𝑇𝑅' = 50 - 6𝑄

c. The derivative of the function 𝑥^2(𝑥^2 + 2𝑥 − 5) is:

𝑥^2(2𝑥 + 2) + (𝑥^2 + 2𝑥 − 5)2𝑥 = 2𝑥^3 + 4𝑥^2 − 10𝑥