“Differentiation from First Principles” starts by illustrating the difficulty of finding a reliable answer for the gradient at a point on a curve by drawing a tangent to the curve. Pupils compare their answers for the gradient at two points on a cubic graph. The method of approximating the gradient of a chord to the gradient of the tangent at a point is then introduced.
Twelve examples are given for pupils to work through (in groups) to find the formula for the gradient at a point on a curve. Hopefully, the connection between the gradient formulae and the original equations will be spotted!
“Differentiation from First Principles” (pdf and ppt versions on 19 pages/slides) is FREE to download.
If you are interested in some revision exercises for A2 classes on different techniques of differentiation then please have a look at “Calculus: Revision Exercises on Methods of Differentiation”. This extensive resource (available in pdf and ppt versions) contains 124 questions in seven exercises (with answers). “Calculus: Revision Exercises on Methods of Differentiation” can be downloaded from Irby Maths’ Shop for £1.80.
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