NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 26

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Question 77:

Find a point on the curve , where the tangent is parallel to the chord joining the points and .

Answer:

Given: Equation of curve,

Firstly, we differentiate the above equation with respect to , we get

Given tangent to the curve is parallel to the chord joining the points and

Put we have

Hence, the tangent to the curve is parallel to chord joining the points and at

Question 78:

Using mean value theorem, prove that there is a point on the curve between the points and , where tangent is parallel to the chord AB. Also, find that point.

Answer:

We have, which is continuous in as it is a polynomial function, Also, , which exists in

By mean value theorem, at which drawn tangent is parallel to the chord AB, where A and B are , respectively.

For

Hence, is the point on the curve between the points where tangent is parallel to the chord AB.

Long Answer (L.A.)

Question 79:

Find the values of and so that

is differentiable at .

Answer:

We have, is differentiable at .