Question
Question: The values of 'a' for which the function f(x) = sin 2x + 2x – ax + b is either always increasing or...
The values of 'a' for which the function
f(x) = sin 2x + 2x – ax + b is either always increasing or always decreasing for all x Î R, are :
A
a < 0 or a > 4
B
0 < a < 1
C
0 < a < 4
D
None of these
Answer
0 < a < 4
Explanation
Solution
f(x) = sin 2x + 2x – ax + b
f '(x) = 2cos 2x + 2 – a
Case-1 f(l) is always increasing
̃ f '(x) > 0 x Î R.
̃ 4cos2x > 0 ̃ a < 0 Min of cos2x = 0
Case-2 f(x) is always decreasing
f '(x) < 0 then
̃ 4cos2x < a ̃ a > 4 Max. of cos2x = 1
Hence a < 0 or a > 4