# Show that the lin

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.

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