IB Maths AI HL 5.4 Tangents and normals Question Bank

Practise IB Maths AI HL 5.4 by analysing tangent and normal geometry in curve, mirror and differential models.

Exam points

Analyse tangent and normal gradients to construct equations at specified points.
Evaluate tangent and normal geometry in applied models, including reflections and differential equations.

[Maximum number: 3]

Consider the curve $y=4 x \sqrt{3 x-2}$ for $x \geq \frac{2}{3}$ .

Hence show that the equation of the tangent to the curve at the point (6,96) is y=25 x-54.

substitution of x=6 into their $\frac{\mathrm{d} y}{\mathrm{~d} x}$
gradient of tangent =(16+9=) 25

Note: Follow through for this A1 from their $\frac{\mathrm{d} y}{\mathrm{~d} x}$ .
at (6,96) tangent is

EITHER
y-96=25(x-6)

OR
$96=25 \times 6+c$

Note: Do not allow follow through for this A1.

THEN
y=25 x-54
AG

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SL 5.4—Tangents and normals question 1