Question

# Let f(x) = cos 2π x+x-[x] ([.] denotes the greatest integer function). Then number of points in [0, 10] in which f  (x) assume its local maximum value, is

A

0

B

10

C

9

D

Infinite

Solution

## The correct option is C 10f (x) = cos (2πx) + {x} f (x) is periodic with period 1 and f (x) has one local maximum in x ε [0, 1].  Maximum in x ε [0, 1]. Hence (b) is the correct answer.

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