... Curves involving x3 + x 1. y = x3 2. y = 2x3 3. y = 4x3 + 2x - 5 Finally, I will summarise my results in a series of tables and work out an overall formula that I could use to predict the gradient of any curve. PART ONE: CURVES CONTAINING X2 (1) y = x2 I am investigating the changes in gradient for the curve y = x2. To plot the curve, I will use the table of values given below. x 0 1 2 3 4 5 6 y 0 1 4 9 16 25 36 I will be working out the gradients of tangents to the curve by using the equation: Gradient = difference in y values difference in x values To help in this, I will draw the tangents to the curve at x values 1 to 4. The gradient of the tangent will equal the gradient of the curve at that point. (1,1) Gradient = difference in y values = 1 = 2 difference in x values 0.5 (2,4) Gradient = difference in ...

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