Gradient Function
My task
My task is to investigate the relationship between the gradients of tangents on the curves of graphs when y=axn
Where a is a constant and is not 0, n is equal to 0, 1, 2, 3………
Definition
Gradient of the curve between x1 and x2 is defined as:
When x2 is getting close to x1 the gradient becomes the gradient of the curve at x1.
The gradient to a curve, at a particular point, is given by the gradient of the tangent to the curve at that point.
Method
- I will draw the curves, y=2x2 and y=ax2 by hand on 5mm graph papers. Next I will draw the tangents and find the gradient of the tangents on the curve when x= -3, -2, -1, 0, 1, 2, 3.
- I will then use the small increment method, where I use a small increment Δx=0.001. For x= -3, -2, -1, 0, 1, 2, 3 I will find the gradient between x and x+Δx by substituting it into the formula, and find Δy/Δx.
