Question #cd906

1 Answer
Oct 25, 2017

Equation of tangent: y=5x-2, equation of normal: y=-\frac{1}{5}x+\frac{16}{5}

Explanation:

Tangents and normals are lines, which means to find their equations we need their gradients and a fixed point, which is (1,3) in this case.

We are given y=3x^2-x+1. Differentiating, we get \frac{dy}{dx}=6x-1. Thus the gradient of the tangent is given by 6(1)-1=5 and the gradient of the normal, perpendicular to the tangent, is given by -\frac{1}{5}. Thus the equation of the tangent is y-3=5(x-1) \Leftrightarrow y=5x-2 and the equation of the normal is y-3=-\frac{1}{5}(x-1) \Leftrightarrow y=-\frac{1}{5}x+\frac{16}{5}.