1. [5 points] Compute the derivative of f (x) = 3x + 8 using the definition of derivative. No marks will be given if any other method is used. Hint: 23 - y3 = (x - y) (22 + xy + y?) 2. [1+2+2 points] Evaluate the derivative of f(x) = _ using the indicated method: (a) Treat f(x) as a power function and apply the power rule. (b) Treat f(x) as a quotient function and apply the quotient rule. (c) Treat f(x) as a product function and apply the product rule. 3. [5 points] Find all the points on the graph of f(x) = x2+ 2x+ 1 whose tangent line goes through the point (-1, -4). Hints: (i) Let (a, f(a)) be an unknown point on the graph of f(x) and find the slope of the line connecting (a, f(a)) to (-1, -4). (ii) Use the derivative to compute the slope of the tangent line to f(x) at the point x = a . (iii) Set these two slope equations equal to each other and solve for a. 4. [5 points] Let C(x) denote the cost function for producing x units of some product. Assuming x > 0, we can define the average cost function C(x) = C(x) Show that the derivative of C(x) is equal to zero whenever C'(x) = C(x)