EduNinja

IB Maths AI SL 5.4 Tangents and Normals

IB Maths AI SL 5.4 Tangents and Normals
IB Mathematics: applications and interpretation guide, first assessment 2021

Practise finding tangent and normal gradients from derivatives and forming their equations through a specified point, including further intersections with the original curve.

How this is tested

  • differentiate and substitute the contact x-coordinate to obtain the tangent gradient
  • use the negative reciprocal for the normal gradient when the tangent gradient is non-zero
  • form the line with point-gradient notation and solve simultaneously for any second intersection

Question 9(c)

[Maximum number: 2]

Consider the function f(x)=x3−2x2+5x−7f(x)=x^{3}-2 x^{2}+5 x-7.

Find the equation of the line that is tangent to the curve y=f(x) at x=1.