IB Maths AI SL 5.4 Tangents and Normals Questions

Practise finding gradients and constructing tangent or normal equations at a point, then verifying them analytically or with technology and interpreting their geometry.

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.

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

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Consider the graph of the cubic function $f(x)=x^{3}+2 x^{2}-4 x-2$ . Part of the graph of y=f(x) is shown in the following diagram.

Figure for Question IB Maths AI SL 5.4 Tangents and Normals Questions question 1 — IB Maths AI SL

Write down

the equation of the tangent.

$\quad y+3=3(x-1)$ OR y=3 x-6

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IB Maths AI SL 5.4 Tangents and Normals Questions question 1