1.

What will be the value of x for which the value of cosx is minimum?(a) 0(b) -1(c) 1(d) Cannot be determinedI have been asked this question in an international level competition.This question is from Calculus Application topic in chapter Application of Calculus of Mathematics – Class 12

Answer»

Correct option is (B) -1

Easiest explanation: Let, f(X) = cosx

Then, f’(x) = -SINX and f”(x) = -cosx

At an extreme point of f(x) we must have,

f’(x) = 0

Or -sinx = 0

Or x = nπ where, n – any integer.

If n is an odd integer i.e., n = 2M + 1 where m is any integer, then at,

x = (2m + 1)π we have, f”(x) = [(2m + 1)π] = -cos(2mπ + π) = -cosπ = -1(-1) = 1

So, f”(x) is positive at x = (2m + 1)π

Hence, f(x) = cosx is MINIMUM at x = (2m + 1)π.

So, the minimum value of cosx is cos(2mπ + π) = cosπ = -1.


Discussion

No Comment Found

Related InterviewSolutions