IB Maths AI HL Sl 5 4 Tangents and Normals Questions

Practise finding gradients and constructing tangent or normal equations, then verifying them analytically or with technology in curve and applied models.

Exam points

Find the gradient at a point and construct the tangent equation.
Construct the normal using the negative-reciprocal gradient and the point of contact.
Use analytic or technology methods to verify the tangent/normal and interpret it geometrically.

Learn this topic

Study SL 5.4—Tangents and normals conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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

All question bank results loaded

Learn this topic

IB Maths AI HL Sl 5 4 Tangents and Normals Questions question 1