Tangent and normal at the same point

Practise tangent and normal at the same point with an original VectorPaths question, worked explanation and related VCE Methods practice.

4 practice marks

Original practice question

Let $f(x)=x^2+1$. Consider the point on the curve where $x=2$. (a) Find the equation of the tangent. [2 marks] (b) Find the equation of the normal. [2 marks]

Worked explanation

• Part (a)

  The point is $(2,5)$ and $f\prime(2)=4$. Thus $y-5=4(x-2)$.

• Part (b)

  The normal gradient is the negative reciprocal $-1/4$. Through $(2,5)$, $y-5=-(x-2)/4$.

(a) $y=4x-3$.; (b) $y=-x/4+11/2$.

Original VectorPaths practice; not an official VCAA question or marking rubric.