Question

What is the number of critical points for f(x) = max(sinx, cosx) for x belonging to (0, 2π)?

(a) 2

(b) 5

(c) 3

(d) 4

The question was posed to me in quiz.

I'm obligated to ask this question of First Order Derivative topic in section Limits and Derivatives of Mathematics – Class 11

Answer 1

Right option is (c) 3

To elaborate: We know that in the range of (0, 2π) the graph of sinx and cosx intersects each other in three points.

And we know that these points of intersection are only the critical points

Thus, there are 3 critical points.