IB Maths AA SL 5.4 Tangents and Normals Questions

Practise finding gradients, equations and interpretations for tangents and normals at a point, using analytic methods or technology where appropriate.

Exam points

Find the gradient f′(a) at a specified point and use point–gradient form to write the tangent equation to y = f(x).
Write the normal equation using the negative reciprocal gradient, checking vertical or horizontal special cases and using analytic methods or technology as permitted.

[Maximum number: 6]

Consider the function $f(x)=\frac{2}{\pi} \sin (3 \pi x)+2$ , where $0 \leq x \leq 2$ . The following diagram shows the graph of f.

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

(a)

Find the gradient of $L_{2}$ .

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substituting their $m_{L_{1}}$ into $-\frac{1}{m_{L_{1}}}$

\left(m_{L_{2}}=\right)-6

(b)

Hence, or otherwise, find the equation of $L_{2}$ .

The line $L_{1}$ intersects the graph of f at another point B , where the x-coordinate of B is greater than 1.5 . This is shown in the following diagram.

Figure for Question (b) — IB Maths AA SL

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IB Maths AA SL 5.4 Tangents and Normals Questions question 1

Question (a)

Question (b)