Show that the line touches the curve at the point where the curve intersects the axis of y.

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.,

Taking out the constant term,

Now differentiating it we get

Now substitute x = 0, we get

Now consider line equation,

We will differentiate this with respect to x, we get

Taking out the constant terms, we get

Line touches the curve if there slopes are equal.

From equation (i) and (ii), we see that

m₁ = m₂

Hence the line touches the curve at the point where the curve intersects the axis of y.