You can see that the gradient function f'(x) of a quartic curve is a cubic curve.
Finally you can investigate higher order curves. In each case, the gradient function f'(x) will be a curve of one order lower.
A graphic calculator may not be allowed in your exam. However you can use one for revision. The TI-83, or similar model, can display graphs and their gradient function for you.
To set this up, go to the Y= screen. Against Y1= enter a simple curve, 3x^2+1 for example. Against Y2= you should make the following selections:
- The function that gives the gradient at any point on a given curve is called the gradient function for that curve
- If the curve is given by y=f(x), then the gradient function is often denoted by f'(x).
- If f(x) is quadratic, then f'(x) is linear
- If f(x) is cubic, then f'(x) is quadratic
- If f(x) is quartic (fourth degree), then f'(x) is cubic
Software/Applets used on this page
The diagram shows a vertical y axis and a horizontal x axis.
Examples: y = 2x, y = 1+x²,
2. A straight line that touches a curve at one point.