CONCAVITY OF CURVE AND POINT OF INFLECTION

Point OF inflection || Question based on Point OF Inflection

Increasing Decreasing Function || Basic Definition || Critical and Stationary Point || Point OF Inflection || Questions Based on Maxima and Minima

Column I, Column II Both x=1a n dx=2 are the points of minima if, p. m is even x=1 is a point of minima and x=2 is a point of inflection if, q. m is odd x=2 is a point of minima and x=1 is point of inflection if, r. n is even Both x=1 and x=2 are the points of inflection if, s. n is odd

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]

Monotonocity || Point OF inflection || Vertical poit || General question

The graph in Fig. shows plot of variation of v with change in u for a concave mirror. Points plotted above the point P on the curve are for values of v : .

Find the critical (stationary ) points of the function f(X)= (x^(5))/(20)-(x^(4))/(12) +5Name these points .Also find the point of inflection

Find the critical (stationary ) points of the function f(X)= (x^(5))/(20)-(x^(4))/(12) +5Name these points .Also find the point of inflection

Find the critical (stationary ) points of the function f(X)= (x^(5))/(20)-(x^(4))/(12) +5Name these points .Also find the point of inflection