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These are the Transum resources related to the statement: "Tangents and normals at a given point, and their equations".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- Differentiation Practise the technique of differentiating polynomials with this self marking exercise.
- Differentiation Video A reminder of how to differentiate different types of functions and how to find the equations of tangents and normals.

Here are some exam-style questions on this statement:

- "
*The table shows some values (rounded to one decimal place) for the function \(y=\frac{2}{x^2}-x, x\neq 0\).*\(x\) -3 -2 -1 -0.5 0.5 1 2 3 4 \(y\) 3.2 2.5 8.5 7.5 1.0 -2.8 *(a) Complete the table of values.*" ... more - "
*Consider the graph of the function \(f(x)=7-3x^2-x^3\)*" ... more - "
*Consider the function \(f(x)=6 - ax+\frac 3{x^2},x\neq 0\)*" ... more - "
*Consider the cubic function \(f(x)=\frac{1}{6}x^3-2x^2+6x-2\)*" ... more - "
*Consider the function \(f(x)=x^3-9x+2\).*" ... more - "
*Let \(f(x)=\frac{g(x)}{h(x)}\), where \(g(3)=36\), \(h(3)=12\), \(g'(3)=10\) and \(h'(3)=4\). Find the equation of the normal to the graph of \(f\) at \(x=3\).*" ... more - "
*Consider the function \(f(x)=\frac{20}{x^2}+kx\) where \(k\) is a constant and \(x\neq0\).*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

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