G X + 530_Assignment_6_Fall2022.pdf x course hero - Google Search 1 / 2 100% + 18 Due: 11:59 pm on Monday, Nov 14, 2022 Section A 1. Consider the functions f(x) = 100 + 22r and g(z) (a) Find f(g(x)) and g(f(z)). (b) Find the inverse of f(x) and g(z). (c) Find the derivative of f(g(r)) with respect to r. (Hint: put g(z) = y; then use the chain rule.) (d) Find the derivative of g(f(x)) with respect to r. (Hint: put f (2) = 2: then use the chain rule.) 2. Find the derivatives of the following functions. (Hint: Use the chain rule.) (a) f(x) = e51 (b) f(x) = (12 - 3x)es (c) f(x) - 2312 (Hint: Take In of both sides and differentiate implicitly) (d) f(x) = 3. Answer the following questions (don't use a calculator; your final answer can have numbers or In functions) (a) eln 40 -? (b) logo.2(z) (c) log. (z) =? (d) In( abyk =? (e) In(1) =? (f) log101 1 =? irch L O O1530_Assignment_6_Fall2022.pdf x course hero - Google Search X + df 2 /2 |- 100% + 1 Find the derivatives of the following functions: (a) y = (1- 2x) 100 (b) y = V2x2 +3 Section C Let f and g be differentiable functions such that f(2) -1, f(0) = =3. f(2) = -3, g(0) -0. s'(0) = -2, g'(1) =2 If h(x) = f(g(x)), compute h'(0). Section D Hints: Profit = Total Revenue - Total Cost; Total Revenue - pf(L); Total cost = w/) A firm produces f(L) = VL + L units of a commodity when L units of labour are employed. The price obtained per unit is p and price per unit of labour is w. (a) What is the profit function I(L)? (b) Find the value of L for which T'(L) = 0. ch O N ENG US