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: 2020-04-19

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)  img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/RES_MATH_AOD_E02_201_Q01.png" width="80%"    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)   img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/RES_MATH_AOD_E02_201_Q02.png" width="80%"       Number of point  of inflection  for  `f(x)  =(x-1)^(3) (x-2)^(2)` is :