CAIE A-Level Mathematics AS 1.7.3 Differentiation Applications Questions

Practise solving numerical methods problems within the AS mathematics syllabus.

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[Maximum number: 4]

Figure for Question CAIE A-Level Mathematics AS 1.7.3 Differentiation Applications Questions question 1 — CAIE A-Level Mathematics AS

The diagram shows the curve with equation $y=9\left(x^{-\frac{1}{2}}-4 x^{-\frac{3}{2}}\right)$ . The curve crosses the x-axis at the point A.

Find the equation of the tangent to the curve at A.

$\frac{\mathrm{d} y}{\mathrm{~d} x}=9\left(-\frac{1}{2} x^{-\frac{3}{2}}+6 x^{-\frac{5}{2}}\right)$
B2, 1, 0
all 3 terms correct: $9,-\frac{1}{2} x^{-\frac{3}{2}}$ and $6 x^{-\frac{5}{2}}$
2 of the 3 terms correct
At x=4 gradient $=9\left(-\frac{1}{16}+\frac{6}{32}\right)=\frac{9}{8}$
Using their x=4 in their differentiated expression
and attempt to find equation of the tangent.
Equation is $y=\frac{9}{8}(x-4)$
or $y=\frac{9 x}{8}-\frac{9}{2} \mathrm{OE}$

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CAIE A-Level Mathematics AS 1.7.3 Differentiation Applications Questions question 1