Pearson Edexcel IAL Mathematics P2.7 Differentiation Question Bank

Practise applying differentiation to curves and practical models, finding stationary points, ranges of increase or decrease, and justified extrema.

Exam points

set dy/dx=0 to find stationary coordinates or unknown values in a model
use d²y/dx² or sign changes to justify a maximum or minimum
solve derivative inequalities to state where a function is increasing or decreasing

Covered syllabus points

P2.7.1 - Applications of differentiation

[Maximum number: 3]

In this question you must show detailed reasoning.

Solutions relying entirely on calculator technology are not acceptable.

Figure 3

Figure 3 shows
- the curve $C_{1}$ with equation $y=x^{3}-5 x^{2}+3 x+14$
- the circle $C_{2}$ with centre T

The point T is the minimum turning point of $C_{1}$
Using Figure 3 and calculus,

find the coordinates of T

The curve $C_{1}$ intersects the circle $C_{2}$ at the point A with x coordinate 2

$y=x^{3}-5 x^{2}+3 x+14 \Rightarrow \frac{\mathrm{~d} y}{\mathrm{~d} x}=3 x^{2}-10 x+3=0$

M1

Roots are $3, \frac{1}{3} \Rightarrow$ when $x=3, y=" 3^{\prime \prime 3}-5 \times " 3^{\prime \prime 2}+3 \times " 3 "+14=\ldots$ .

dM1

Centre is (3,5)

A1

(3)

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Covered syllabus points

P2.7 - Differentiation question 1