Write sufficient conditions for a point `x=c` to be a point of local maximum.

Write necessary condition for a point x=c to be an extreme point of the function f(x) .

Examine the graph of following functions in each case identify the points of global maximum // minimum and local maximum // minimum.

The function f(x)=|x^2-2|/|x^2-4| has, (a) no point of local maxima (b) no point of local minima (c) exactly one point of local minima (d) exactly one point of local maxima

if lim_(h->0) [f(a-h)/f(a)]=c where f(x) is a continuous function such that f(x)> 0 for all x in R and [.] denotes greatest integer function then which of the following statements is always true ? (A) If x=a is a point of local minima then c in N (B) if x = a is a point of local maxima then c in N (C) If x=a is a pioint of local minima then c in I (D) If x= a is a point of local maximka then c in I

For the function f(x)=x+1/x x=1 is a point of maximum (b) x=-1 is a point of minimum (c) maximum value > minimum value (d) maximum value < minimum value

The function S(x)=int_(0)^(x)sin((pit^(2))/(2)) dt has two critical points in the interval [1,2.4] . One of the critical points is a local minimum and the other is a local maximum . The local maximum occurs at x equals _____

Suppose f(x) is differentiable at x=a . Then , necessary condition for f(x) to possess local maxima or local minima at x=a is

In each of following graphs identify if x= a is point of local maxima minima or neither

Write the distance of a point P(a ,b ,c) from x-axis.

Draw graph of f(x) =x|x-2| and hence find points of local maxima // minima.