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

Concavity and convexity : if f''(x) gt 0 AA x in (a,b) then the curve y=f(x) is concave up ( or convex down) in (a,b) and if f''(x) lt 0 AA x in (a,b) then the curve y=f(x) is concave down (or convex up ) in (a,b) Inflection point : The point where concavity of the curve changes is known as point of inflection (at inflection point f''(x) is equal to 0 or undefined) Exhaustive set of values of 'a' for which the function f(x) =x^(4) +ax^(3)+(3x^(2))/(2)+1 will be concave upward along the entire real line is :

Concavity and convexity : if f''(x) gt 0 AA x in (a,b) then the curve y=f(x) is concave up ( or convex down) in (a,b) and if f''(x) lt 0 AA x in (a,b) then the curve y=f(x) is concave down (or convex up ) in (a,b) Inflection point : The point where concavity of the curve changes is known as point of inflection (at inflection point f''(x) is equal to 0 or undefined) Exhaustive set of values of 'a' for which the function f(x) =x^(4) +ax^(3)+(3x^(2))/(2)+1 will be concave upward along the entire real line is : (A) [-1,1] (B) [-2,2] (C) [0,2] (D) [0,4]

Find the number of integral vaues of 'a' for which the range of function f (x) = (x ^(2) -ax +1)/(x ^(2) -3x+2) is (-oo,oo),

Find the number of integral vaues of 'a' for which the range of function f (x) = (x ^(2) -ax +1)/(x ^(2) -3x+2) is (-oo,oo),

Find the values ' a ' for which the function f(x)=(a+2)x^3-3a x^2+9a x-1 decreases for all real values of x .

Find the values of a for which the function f(x)=(a+2)x^3-3a x^2+9a x-1 decreasing for all real values of xdot

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,

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,