Solve for the following

Consider the cubic function f(x) = 6x*+ 11x2 -4x -4. a) Show that f(x) = 0 when x = -2. b) Show algebraically that: f(x +h) = 6x3+ 18hx3+11x2+18h2x+22hx -4x+6h3+11h- - 4h - 4. Hint: (xth]]=x +3hx-+3h2x+43. c) The gradient of the secant between any two points (x1, f(x1)) and (x2, f(x2)) on the function can be calculated using a dif- ference quotient: f(xx2) - f(x1) X2 - X1 Use this difference quotient to calculate the gradient of the secants when: i) x1 = 1 and x2 = 1.01. ii) x1 = 1 and x2 = 1.001. iii) x1 = 1 and x2 = 1 + h. Do NOT round your answers. d) Use your answer to Q5c. (iii) to show that at x = 1 as h - () the difference quotient approaches 36. e) Find f'(x) and evaluate the derivative when x = 1. f) Explain in general terms the meaning of the derivative. g) Find F(x). h) i) Solve 2 f(x)dx. ii) In general terms, what does the solution to Q5h.(i) rep- resent