Question

Using Lagrange’s mean-value theorem, find a point on the curve y = x², where the tangent is parallel to the line joining the point (1, 1) and (2, 4)

Answer 1

Given: y = x²

Since y is a polynomial function.

It is continuous and differentiable in [1,2]

So, there exists a c such that:

So, the point is (3/2, 9/4)