The number of nonzero integral values of `a` for which the function `f(x)=x^4+a x^3+(3x^2)/2+1` is concave upward along the entire real line is___________

The number of integral values in the range of the function f(x)=sin^(-1)x-cot^(-1)x+x^(2)+2x +6 is

Verify mean value theorem for the function f(x) = x^(3) - 5x^(2) _ 2x in [1, 3]

If graph of the function f(x) = 3x^(4)+2x^(3)+ax^(2)-x+2 is concave upward for all real x, then find values of a,

Find the value of a for which the function (a+2)x^3-3a x^2+9a x-1 decreases montonically for all real xdot

Find the real values of x for which the function f(x) = cos^(-1) sqrt(x^(2) + 3 x + 1) + cos^(-1) sqrt(x^(2) + 3x) is defined

consider the function f(X) = 3x^(4)+4x^(3)-12x^(2) The range of the function y=f(x) is

Integrate the functions (x+3)/(x^(2)-2x-5)

Integrate the functions (3x)/(1+2x^(4))

Integrate the function (3x^(2))/(x^(6)+1)

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is (a)2 (b) 0 (c) 4 (d) 1