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.
Summary/Background
A graphic calculator may not be allowed in your exam. However you can use one for revision. The TI83, 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
Glossary
cubic
equation
function
gradient
graph
The diagram shows a vertical y axis and a horizontal x axis.
linear
polynomial
Examples: y = 2x, y = 1+x²,
quadratic
tangent
2. A straight line that touches a curve at one point.