Let f(b) be the minimum value of the expression `y=x^(2)-2x+(b^(3)-3b^(2)+4)AA x in R`. Then, the maximum value of f(b) as b varies from 0 to 4 is

The maximum value of f(x)=2bx^(2)-x^(4)-3b is g(b), where b>0 If b varies,then maximum value of g(b) 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 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(x0=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

Let f(x)=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f (x). As b varies, the range of m (b) is

If the HCF of 8x^(3)y^(a) and 12x^(b)y^(2) is 4x^(a)y^(b) find the maximum value of a+b

Let f(x) is ax^(2)+bx+c;(3a+b>0) and f(x)>=0 AA x in R, then minimum value of (4a+2b+c)/(3a+b) is

Let f(t) be the minimum value of |3sin x-4cos x+t+(4)/(t)| where x,t in R . If the value of int_(1)^(10)f(x)dx = 4(a+ln b), where a,b in Q, then find the value of (a+2b)