The function `f(x)=x^(3)+ax^(2)+bx+c,a^(2)le3b` has

The function f(x) =x^3+ax^2+bx+c,a^2lt=3b has

The function f(x)=4x^(3)+ax^(2)+bx+2 has an extremum at (2,-2) , find the values of a and b . Show that , the function possesses a minimum value at the extreme point.

If the function f(x)=4x^(3)+ax^(2)+bx-1 satisfies all the conditions of Rolle's theorem in -(1)/(4) le x le 1 and if f'((1)/(2))=0 , then the values of a and b are -

Find the condition so that the function f(x)=x^(3)+ax^(2)+bx+c is an increasing function for all real values of x.

If the conditions of Rolle's theorem are satisfied by the function f(x)=x^(3)+ax^(2)+bx-5 in 1 le x le 3 with c=2+(1)/(sqrt(3)) , then the values of a and b are -

Rolle's theorem hold for the function f(x)=x^(3)+bx^(2)+cx,1 le x le2 at the point 4/3, the values of b and c are

Rolle's theorem holds for the function f(x)=x^(3)+bx^(2)+cx, 1 le x le 2 at the point (4)/(3) , the values of b and c are :

If the function f(x)=x^(3)+ax^(2)-bx+4 defined in -2 le x le 2 satisfies Rolle's theorem when -2 lt c lt 2 where c=(1)/(3)(1+sqrt(13)) , then find the values of a and b.

The possible value of the ordered triplet (a, b, c) such that the function f(x)=x^(3)+ax^(2)+bx+c is a monotonic function is