Differentiation (Edexcel IGCSE Further Pure Maths): Exam Questions

Show that

The curve has equation

Using calculus, find the exact value of the gradient of the tangent to when

Show that where and are integers to be found.

Find

Give your answer in the form where , and are prime numbers to be found.

The value of increases by 2%

Use your answer to part (a) to find an estimate, in terms of , for the percentage change in
Give your answer in the form where and are integers.

Show that

Hence show that

Figure 3 shows part of the curve with equation
The curve crosses the -axis at the point and the -axis at the point .

(i) Write down the coordinate of point .

(ii) Show that the coordinate of is