CAIE IGCSE Mathematics Extended E2.12 Differentiation Topic Practice

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Covered syllabus points

E2.12.1 Estimate gradients using tangentsE2.12.2 Differentiate simple power functionsE2.12.3 Gradients and stationary pointsE2.12.4 Distinguish maxima and minima

Question 1

[Maximum number: 3]

The diagram shows the graph of y=f(x) for −3⩽x⩽3-3 \leqslant x \leqslant 3.

Figure for Question 1 — CAIE IGCSE Mathematics Extended

By drawing a suitable tangent, find an estimate of the gradient of the graph
at the point ( -2,4 ).

Question 2

[Maximum number: 5]
Figure for Question 2 — CAIE IGCSE Mathematics Extended

The diagram shows a sketch of y=18+5x−2x2y=18+5 x-2 x^{2}.

Question (a)

(a)

Differentiate 18+5 x-2 x^2.

[ 2 ]

Question (b)

(b)

Find the coordinates of the point on y=18+5 x-2 x^2 where the gradient is 17 .

[ 3 ]

Question 3

[Maximum number: 5]
Figure for Question 3 — CAIE IGCSE Mathematics Extended
f(x)=x(x+2)(x−3)\mathrm{f}(x)=x(x+2)(x-3)

A is the point (1,-6).

The tangent to the graph of y=f(x) at A meets the y-axis at B.
Find the coordinates of B.
(

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