The maximum value of `f(x) = 2bx^2 - x^4 -3b` is g(b), where `b gt 0`. If b varies, then maximum value of g(b) is

For real number x, if the minimum value of f(x) =x^(2) +2bx +2c^(2) is greater than the maximum value of g(x) =-x^(2)-2cx+b^(2) , then

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

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

If A gt 0, b gt 0 and A+B =pi//3 , then the maximum value of tan A tan B is

If minimum value of f(x)=x^(2)+2bx+2c^(2) is greater than maximum value of g(x)= -x^(2)-2cx +b^(2) , then for x is real :

Assertion (A) : The maximum value of quadratic function -x^(2)+3x+1 is (11)/(4) Reason (R ) : The maximum value of ax^(2)+bx+c is (4ac-b^(2))/(4a) if alt0

Let A = [{:(2, b,1),(b, b^(2)+1,b),(1, b,2):}], " where "b gt 0 . Then, the maximum value of ("det"(A))/(b) is

If minimum value of f(x)=(x^(2)+2bx+2c^(2)) is greater than the maximum value of g(x)=-x^(2)-2cx+b^(2) , then (x in R)