Concavity and convexity : if `f\'\'(x) gt 0 AA x in (a,b)` then the curve y=f(x) is concave up (
Channel: Doubtnut
Date: 2020-01-26

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 :