Let `f(x) =` Maximum `{sin x, cos x} AA x in R`. minimum value of `f (x)` is

Let f(x)=max{|sin x|,|cos x|}AA x in R then minimum value of f(x) is

For any real number b, let f (b) denotes the maximum of |sin x+(2)/(3+sin x)+b|AA x in R. Then the minimum vlaue of f (b) AA b in R is:

For any real number b, let f (b) denotes the maximum of | sin x+(2)/(3+sin x)+b|AAxx x in R. Then the minimum value of f (b)AA b in R is:

Let f(x) = cos(x) + cos(sqrt(3)x) AA x in R . The number of values of x for which f(x) is maximum is

For any ral number b, let f (b) denotes the maximum of | sin x+(2)/(3+sin x)+b|AAxx x in R. Then the minimum valur of f (b)AA b in R is:

Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in R and is strictely increasing function. If the range of a is [(m)/(n),oo), then find the minimum vlaue of (m- n).

Let f (x) = ax+cos 2x +sin x+ cos x is defined for AA x in R and a in R and is strictely increasing function. If the range of a is [(m)/(n),oo), then find the minimum vlaue of (m- n).

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is