(a) Let f(x) = √√3x + 1. Use the definition of derivative to differentiate f(x), and then find the tangent line to the graph of y = f(x) at x = 4. (5 marks) (b) Consider the function f(x) = 4x5 - 4x³.

(i) Find the x-intercepts and y-intercepts. (2 marks)

(ii) Find the intervals over which the function f(x) is increasing and the intervals on which it is

decreasing. (3 marks)

(iii) Find local minimum/maximum points. (3 marks)

(iv) Find the intervals over which the function f(x) is concave upwards and the intervals on which it is concave downwards. (3 marks)

(v) Determine the points of inflection of f(x). (2 marks)

(vi) Sketch f(x) showing all intercepts, turning points and points of inflection. (2 marks)