Question

If differentiation of any function is infinite at any point and constant at other points then it means ___________

(a) Function is parallel to x-axis at that point

(b) Function is parallel to y-axis at that point

(c) Function is constant

(d) Function is discontinuous at that point

This question was addressed to me during an online interview.

Query is from Improper Integrals topic in chapter Integral Calculus of Engineering Mathematics

Answer 1

Correct option is (a) Function is parallel to x-axis at that point

To explain: Since slope of a function is given by ^dy⁄dx at that point.Hence,when ^dy⁄dx = ∞ means slope of a function is 90 degree i.e,parallel to y axis.