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