Q15 of 292 Page 490

Using Lagrange’s mean-value theorem, find a point on the curve , where the tangent is parallel to the line joining the point (1, 1) and (2, 4)

Given:

y=x²

Since y is a polynomial function.

It is continuous and differentiable in [1,2]

So, there exists a c such that:

⇒ f' (c)=2c

⇒ 2c=3

So, the point is

14 B

Find ‘c’ of Lagrange’s mean-value theorem for

14 C

Find ‘c’ of Lagrange’s mean-value theorem for

Find a point on the curve , where the tangent to the curve is parallel to the chord joining the points (1, 1) and (3, 27).

Find the points on the curve , where the tangent to the curve is parallel to the chord joining (1, −2) and (2, 2).