Definition of Gradient (Edexcel AS Maths): Revision Note
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Definition of Gradient
What is the gradient of a curve?
At a given point the gradient of a curve is defined as the gradient of the tangent to the curve at that point
A tangent to a curve is a line that just touches the curve at one point but doesn't cut the curve at that point
A tangent may cut the curve somewhere else on the curve
It is only possible to draw one tangent to a curve at any given point
Note that unlike the gradient of a straight line, the gradient of a curve is constantly changing
Examiner Tips and Tricks
A tangent only exists at points where a curve is smooth.
For example, there is no tangent (or gradient) at one of the 'corners' in a modulus function.
Worked Example
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