Question

If A (x1, y1) and B (x2, y2) be two points on the curve y = ax^2 + bx + c, then as perLagrange’s mean value theorem whichof the following is correct?

(a) At least one point C(x3, y3) where the tangent will be intersecting the chord AB

(b) At least one point C(x3, y3) where the tangent will be overlapping to the chord AB

(c) At least two points where the tangent will be parallel to the chord AB

(d) At least one point C(x3, y3) where the tangent will be parallel to the chord AB

The question was posed to me in an online quiz.

This key question is from First Order Derivative in section Limits and Derivatives of Mathematics – Class 11

Answer 1

The correct option is (d) At least one point C(x3, y3) where the tangent will be parallel to the chord AB

The best I can explain: Here, y = f(x) = ax^2 + bx + c

As f(x) is a polynomial function, it is continuous and differentiable for all x.

So, according to geometrical interpretation of mean value theorem there will be at least one point C (x3, y3) between A (x1, y1) and B (x2, y2) where tangent will be parallel chord AB.