The set of values of p for which the points of extremum of the function, `f(x) = x^3 -3px^2 + 3 (p^2 -1)x + 1` lin in the interval `(-2,4)` is

The set of values of p for which the points of extremum of the function,f(x)=x^(3)-3px^(2)+3(p^(2)-1)x+1lin in the interval (-2,4) is

The number of points of extremum of the function f(x)=(x-2)^(2/3)(2x+1) is

The value of a for which all extremum of function f(x)=x^(3)+3ax^(2)+3(a^(2)-1)x+1 , lie in the interval (-2, 4) is

The value of a for which all extremum of function f(x)=x^(3)+3ax^(2)+3(a^(2)-1)x+1 , lie in the interval (2, 4) is

The value of a for which all extremum of function f(x)=x^(3)+3ax^(2)+3(a^(2)-1)x+1 , lie in the interval (2, 4) is

The value of a for which all extremum of function f(x)=x^(3)-3ax^(2)+3(a^(2)-1)x+1 lie in the interval (2,4) 1) (3,4) 2) (-1,3) 3) (-3,-1) 4) none of these

The greatest value of the function f(x)=2. 3^(3x)-3^(2x). 4+2. 3^x in the interval [-1,1] is

verify mean value therem for the function f(x) = x^2 -4x -3 in the interval [1,4]

The set of values of p for which x^(2)-2px+3p+4 is negative for atleast one real x is