Consider on the interval

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

Problem

Consider y=sec⁡xy=\sec x on the interval (−π2,π2)\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right). Which of the following statements about the concavity of the graph is correct? (a) The graph alternates between concave up and concave down infinitely many times within the interval. (b) The graph is concave down on the entire interval and has no points of inflection. (c) The graph is concave up on the entire interval and has no points of inflection. (d) The graph is concave up on (−π2,0)\left(-\dfrac{\pi}{2},0\right) and concave down on (0,π2)\left(0,\dfrac{\pi}{2}\right) with an inflection point at x=0x=0.

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