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The number of nonzero integral values of...

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___________

A

`a in [0,oo)`

B

`a in (-2, 2)`

C

`a in [-2, 2]`

D

`a in (0, oo)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • 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 :

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

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  • The interval into which the function y =(x -1)/(x^2 - 3x + 3) transforms the entire real line is

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