(Differential Calculus) Please answer the question **ON PAPER**

FUNCTION GRADIENT FUNCTION y = 2x y = 2 y = x - 2 y = 2x y =- 5x2+4 y = - xy=x4+lx3+2x24x3 y=4x3+12x2+4x4 Can you see a pattern? ie. 0 Can you see the correlation between the value of the gradient, whether it is positive or negative, and the original curve? 0 What is special about the x-interoepts of the gradient function? 0 What is the relationship between the degree of the polynomials? Develop a rule for finding the gradient function of y = a\" Part 1 For the following functions f(x) = 3x - 1, f(x) = 3x + 4 and f(x) = 3x + 1 (a) Find the derivative for all three using rst principles. (b) What do you notice? (c) Why is this the case? Prove your answer by graphing the functions. Part 2 Here are the graphs of some functions, and their matching "gradient functions". Follow the curves along simultaneously, can you see the correlation between the value of the gradient, whether it is positive or negative, and the original curve. What is special about the xintercepts of the gradient function