5.4 Tangents and normalsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 5.4 Tangents and normals

1. 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
2. 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
3. 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