QUESTION 3 a) Given a function f (x) = 5 x - 5 i) Find y-intercept. (2 marks) ii) Determine the interval(s) where f is increasing or decreasing given the critical value is x = -5. (4 marks) ii) Determine the interval(x) where f is convave up or concave down given the critical value is x = -5. (3 marks) iv) Sketch the graph given the horizontal asymptote is y =0 and vertical asymptote is x = -5. (3 marks) b) Suppose that z = 3x3 - x2 + 10x, where both z and x are both functions of time t. Given that x is increasing at the rate of 2 units/sec. How fast is z changing when x = 4? (4 marks) c) The surface area of a closed box is given as $ = 2x2 + 32000 , find the dimensions of the box that minimize the amount of material used. (5 marks) QUESTION 4 a) Evaluate the following integrals: i) (5x-6vx + 2x3 -x +10 - dx (6 marks) ii) sinx dx (cosx + 5)7 (5 marks) b) Given F(x) = 6 VE-2 ' (x 407- Use the Second Fundamental Theorem of Calculus to find F(10). Hint : & Jr(jar - "(s( x ) de (5 marks) c) Evaluate "ME 512 + 2i