Question

Find the equation of the tangent to the curve y(x – 2)(x – 3) – x + 7 = 0 at the point where it cuts the x-axis.

Answer 1

The curve cuts the x-axis at y = 0. 

But y = 0 implies –x + 7 = 0 or x = 7 

Thereby means tangent is taken at the point (7, 0) 

The equation of the tangent at (7, 0), however, is given by

or 

= 0  is the desired equation of tangent at (7, 0).