5.4 Tangents and normalsIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What is the gradient of the tangent to y=f(x) at x=a?
What is the normal to a curve at a point?
How do you find the gradient of the normal?
Product of the gradients of two perpendicular lines?
Equation of a line through (x1,y1) with gradient m?
Steps to find the equation of a tangent?
Tangent gradient 8. What is the normal gradient?
What if f'(a)=0?
How do you find where the tangent has gradient k?
How do you find where a tangent meets the x-axis?
What can a GDC do for tangents?
A tangent is parallel to y=3x+1. What do you know?

Exam questions on 5.4 Tangents and normals

The curve $C$ has equation $y=x^3-4x+1$ and passes through the point $P(2,1)$ .
Find the equation of the tangent to $C$ at $P$ , giving your answer in the form $y=mx+c$ .2 marks
A curve has equation $y=2x^2-5x+3$ .
Find the equation of the tangent to the curve at the point where $x=3$ . Give your answer in the form $ax+by+d=0$ , where $a$ , $b$ and $d$ are integers.2 marks
A curve has equation $y=x^3-3x^2+2x+4$ . The point $A$ on the curve has $x$ -coordinate $3$ .
Find the equation of the tangent to the curve at $A$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).