If f(x)=x-3x, find the solutions to f'(x) = 0. Problem 2 Compute the first-order derivatives for the following functions: (a) y=2x-5 (b) y = x (e) y=(x-5) (f) y=x-x-5 Problem 3 (a) Let C(Q) denote the cost of producing Q units per month of a commodity. What is the interpretation of C'(1000) 25? Suppose the price obtained per unit is fixed at 30 and that the current output per month is 1000. Is it profitable to increase production? (b) A firm's profit function is (Q) = 24Q-Q-5. Find the marginal profit and the value Q* of Q, which maximizes profits. (c) A firm's revenue function is R(Q) = 5000-Q. Find the marginal revenue. (d) For the particular cost function C(Q) = -Q3+214.20-79000+ 320 700, find the marginal cost. Problem 4 Examine where the following functions are increasing/decreasing (a) f(x) = x-6x+5 (b) f(x)=-2(x+2)(x-6) Problem 5 A function has derivative f'(x)=2(x+2)(4-x)(x-6). Examine where the function is increasing/ decreasing. Problem 6 Differentiate the following functions w.r.t. x: (a) x+1 (b) x+x (c) 3x+2x+5 (d) 8x4 +2x (e) x-x+5x (f) 1-3x7 Course: ECO10002 Instructor: Marian Melnyk Problem 7 Differentiate the following functions w.r.t. x: (a) x-2x+-x Problem 8 (b) (2x21)(x1) (c) ) (x + = ) (x + 1) Differentiate the following functions w.r.t. x: -18 (b) x(x+1)x Problem 9 Differentiate the following functions w.r.t. x: x-2 (a) x+1 Problem 10 Compute the following limits: (a) lim (x+3x-5) -13 1 x+x+1 (b) (c) x+1 x-x+1 (b) lim x-2x-1 x-2 (c) lim y-3y+8 x0 x-x-1 x +3x - 2x (d) lim (x+h)-x x0 (e) lim x h0 h