1 Differentiation
The value of 'a' in order f(x)= √ 3?sinx−cosx−2ax+b decrease for all real values of x, is given by
1) a > 1 2) a ≥ 1 3) a ≥ 2 4) a < 2
SOLUTION
Given, f(x)= √ 3?sinx−cosx−2ax+b
f′(x)=√3?cosx+sinx−2a
f′(x)=2((√3 /2)cosx + (1 /2)sin x) - 2a
f′(x)=2(sin(π / 3 ? + x )−a)
if a>1, then for all real values of x ,f′(x)<0.
So, a>1
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