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tangent and normal
To find the gradient of a tangent to a curve y=f(x) at a given point x=a:
firstly differentiate the equation of the curve in order to find \displaystyle\frac{dy}{dx} ,
secondly substitute into this expression the value x=a.
    

Summary/Background

If y = ax^n then \displaystyle\frac{dy}{dx} = anx^{n-1} and if y = a then \displaystyle \frac{dy}{dx} = 0, where a is a constant.
These work for all values of n, positive or negative, decimal or fraction.

Software/Applets used on this page

jsMath
This page uses jsMath You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

Glossary

differentiate

to find the derivative of a function

equation

A statement that two mathematical expressions are equal.

gradient

The slope of a line; the angle of its inclination to the horizontal.

tangent

1. The trigonometrical function defined as opposite/adjacent in a right-angled triangle.
2. A straight line that touches a curve at one point.

work

Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.