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Concavity and convexity : if f''(x) ...

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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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) Number of point of inflection for f(x) =(x-1)^(3) (x-2)^(2) is :

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