Question

Using mean value theorem, prove that there is a point on the curve y = 2x² – 5x + 3 between the points A(1, 0) and B(2, 1), where tangent is parallel to the chord AB. Also, find that point

Answer 1

We have, y = 2x² – 5x + 3, which is polynomial function.

So it is continuous and differentiable.

Thus conditions of mean value theorem are satisfied.

Hence, there exists atleast one c ∈ (1, 2) such that,

f'(c) = `("f"(2) - "f"(1))/(2 - 1)`

⇒ 4c – 5 = `(1 - 0)/1`

⇒ 4c – 5 = 1

∴ c = `3/2 ∈ (1, 2)` 

For x = `3/2`, y = `2(3/2)^2 - 5(3/2) + 3` = 0

Hence, `(3/2, 0)` is the points on the curve y = 2x² – 5x + 3 between the points A(1, 0) and B(2, 1), where tangent is parallel to the chord AB.