(differential calculus) (Rates)

Please answer all the following questions *On paper*

Here is a graph of the cubic function y = x3 -2 1.75 .-1.5 -1.25 -1 . 41.5 25 0 D25 .05 0.75 . 1 .125 .1.5 1.75 i 2 1. You are to draw (as best as possible using a ruler), tangents at the positions as indicated in this table, and calculate the gradient of those tangents (remember: gradient of a straight line is rise/run) and ll in the relevant row. X (coordinate) Y (coordinate) Gradient of the tangent (riselrun) 3dp accuracy 2. Draw a graph of x vs the gradient value. 0n the x-axis use the same x- values, on the y - axis instead of drawing the graph y = x3, you are going to draw a graph of the gradient. Plot the points (x, gradient). 9 a 1 a 5 4 a 2 II a -1 .2 -3 .4 -5 .a .1 -a 43 3. Write a comment here about what you have found, what does it look like? 4. What sort of function have you found? - Can you nd the equation of it? (This is the equation of the gradient function) 5. From your equation and/or graph, predict the gradient at x = 1.5 Calculate the gradient on your rst graph. Does it match