Given: two curves and
To prove: Two curves have the possibility of meeting at a point(1,2)
Explanation:
Now given
Differentiating the above equation with respect to x
Now using the sum rule of differentiation
Also given
Differentiating the value with respect to x, we get
Using a product rule of differentiation, we get
Finding the solution of the above equation at point (1,2), we get
From equation (i) and (ii),
∴
Therefore it is possible for both the curves to touch each other at points (1,2).
Hence proved