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These are the Transum resources related to the statement: "Understand and use the derivative of f (x) as the gradient of the tangent to the graph of y = f ( x) at a general point (x, y); the gradient of the tangent as a limit; interpretation as a rate of change, sketching the gradient function for a given curve, second derivatives, differentiation from first principles for small positive integer powers of x and for sin x and cos x. Understand and use the second derivative as the rate of change of gradient; connection to convex and concave sections of curves and points of inflection".

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

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

Here are some exam-style questions on this statement:

- "
*A function is given as \(f(x)=3x^2-6x+4+\frac3x,-2\le x \le 4, x\ne 0\).*" ... more - "
*Consider the graph of the function \(f(x)=7-3x^2-x^3\)*" ... more - "
*A child's play tent is made in the shape of half a cylinder. It is constructed from a fibreglass frame with material pulled tightly around it. The fibreglass frame consists of a rectangular base, two semi-circular ends and two further support rods, as shown in the following diagram.*" ... more - "
*A package is in the shape of a cuboid and has a length \(l\) cm, width \(w\) cm and height of 12 cm.*" ... more - "
*Consider the function \(f(x)=6 - ax+\frac 3{x^2},x\neq 0\)*" ... more - "
*If \(f(x)=xsinx\), for \(-3\le x\le3\)*" ... 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 - "
*The function \(f\) is defined as follows:*" ... more - "
*Consider the functions*" ... more - "
*Let \(f(x)=jx^3+jx^2+kx+m\) where \(j, k\) and \(m\) are constants.*" ... more - "
*The following diagram shows part of the graph of \(y=f (x)\)*" ... more - "
*Let \(f(x) = \frac{ln3x}{kx} \) where \( x \gt 0\) and \( k \in \mathbf Q^+ \).*" ... 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.

This video on the Basics of Differentiation is from Revision Village and is aimed at students taking the IB Maths Standard level course

If you use a TI-Nspire GDC there are instructions useful for this topic.

This video on Optimization and Calculus Curves is from Revision Village and is aimed at students taking the IB Maths AA SL/HL course.

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.