Questions 5 to 7

5. Let f(x) = -5x2 + 3.r and g(x) = Vx - 3 (a) Find f'(x) and g'(x) by using the definition of the derivative. (No marks will be given for the use of any differentiation rules.) (b) Find f'(-2) and f'(0). (c) Find the average rate of change of f over the interval [2, 5]. (d) Find the instantaneous rate of change of g at r = 12. (e) Find the slope of the tangent line to the graph of f at z = 7. (f) Find the equation of the tangent line to the graph of g at P(4, 1). (g) Does g'(3) exist? Justify your answer. 6. Show that the function f(x) = (x - 2) is not differentiable at r = 2. I THE UNIVERSITY OF BRITISH COLUMBIA OKANAGAN MATH 116 - Calculus I 7. Shown is the graph of a function f and its derivative f'. Decide which graph is that of f and which is the graph of f'. Justify your answer. -30