At their intersection point

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

At their intersection point (x0,y0)(x_0, y_0), two differentiable curves are said to share a common tangent. Which of the following conditions must hold at (x0,y0)(x_0, y_0)? (a) Their second derivatives are equal at (x0,y0)(x_0,y_0). (b) Their slopes are equal at (x0,y0)(x_0,y_0). (c) The product of their slopes at (x0,y0)(x_0,y_0) equals −1-1. (d) The magnitudes of their slopes are equal at (x0,y0)(x_0,y_0).

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