Answer :

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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