If `f(x)=x^3+3x^2+4x+ bsinx+ c cosx AA x in R` is a one-one function then the value of `b^2 + c^2` is

If f(x)=x^(3)+3x^(2)+4x+asinx+bcosx, forall x in R is a one-one fuction, then the greatest value of (a^(2)+b^(2)) is

If f(x)=x^(3)+3x^(2)+4x+asinx+bcosx, forall x in R is a one-one fuction, then the greatestn value of (a^(2)+b^(2)) is

f(x) =x^3/3+x^2/2+ax +b,AAx inR. If (x) is one one function then the minimum value of a is ........

If f(x)=x^(3)+ax^(2)+bx+5sin^(2)x, AA x in R is an increasing function, then …………..

If f (x) +2 f (1-x) =x ^(2) +2 AA x in R and f (x) is a differentiable function, then the value of f'(8) is

Consider the function f(x)=tan^(-1){(3x-2)/(3+2x)}, AA x ge 0. If g(x) is the inverse function of f(x) , then the value of g'((pi)/(4)) is equal to

Consider the function f(x)=tan^(-1){(3x-2)/(3+2x)}, AA x ge 0. If g(x) is the inverse function of f(x) , then the value of g'((pi)/(4)) is equal to

It is given that the Rolles theorem holds for the function f(x)=x^3+b x^2+c x ,\ \ x in [1,2] at the point x=4/3 . Find the values of b and c .

It is given that the Rolles theorem holds for the function f(x)=x^3+b x^2+c x ,\ \ x in [1,2] at the point x=4/3 . Find the values of b and c .