Given: equation of line the curve intersects the y-axis
To show: the line touches the curve at the point where the curve intersects the axis of y
Explanation: given the curve intersects the y-axis, i.e., at x = 0
Now differentiate the given curve equation with respect to x, i.e.,
Then considering the line equation,
Line touches the curve only if their slopes are equal
From equation (i) and (ii), we see that
Hence, the line touches the curve at the point where the curve intersects the axis of y.