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)

Question

Philoid · Accepted Answer

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