1 − x2 < cos x. Squaring gives 1 − x2 < cos2 x. This can be proved using the principles of problems. 6 and 7. The derivative of cos2 x − (1 − x2) is twice the ...

We will mainly focus on nicely behaved functions which are differentiable at each point of their domains. Some of the examples are very straightforward, while ...

Question 1 (non calculator). For each of the following curves find an equation of the tangent to the curve at the point whose x coordinate is given.

A curve whose equation is has stationary points at (−0.5, 1.75) and (1, −5). Determine the nature of these points. Solution. We solved this problem by using ...

The volume of a cylinder is given by the formula V = πr2h. Find the greatest and least values of V if r + h = 6. Solution. For questions alike, we need to re ...

In this Workbook you will learn to apply your knowledge of differentiation to solve some basic problems connected with curves. First you will learn how to ...

Practical Applications of Differentiation. Q1, (OCR 4752, Q10). Q2, (Edexcel 6664, Jun 2015, Q9). Page 2. ALevelMathsRevision.com. Q3, (Edexcel 6664, Jan 2011 ...

Read each question carefully before you begin answering it. 2. Check your answers seem right. 3. Always show your workings. Revision for this topic.

[2]. (ii). Use differentiation to find, in terms of 𝑎, the value of 𝑥 that gives a maximum possible value of 𝑉, proving that it is a maximum. [5]. [The volume ...

Differentiate 2x3 + 9x2 − 24x. Hence find the set of values of x for which the function f(x) = 2x3 + 9x2 − 24x is increasing. 2.