Let `f(x)=x^(3)-3x^(2)+6` find the point at which f(x) assumes local maximum and local minimum.

Let f:IRrarrIR be defined as f(x)=|x|+|x^2-1| .The total number of points at which f attains either a local maximum or a local minimum is

Let f(x)=(x-1)^m(x-2)^n,"x"inR then each critical point of f(x) is either local maximum or local minimum where

Let f(x)=-sin^3x+3sin^2x+5 on [0,pi/2] . Find the local maximum and local minimum of f(x)dot

Let f(x) be a cubic polynomial which has local maximum at x=-1 \ and \ f(x) has a local minimum at x=1. if f(-1)=10 \ and \ f(3)=-22 , then one fourth of the distance between its two horizontal tangents is ____________

f has a local maximum at x = a and local minimum at x = b. Then -

If f(x)=(sin^2x-1)^("n"),"" then x=pi/2 is a point of local maximum, if n is odd local minimum, if n is odd local maximum, if n is even local minimum, if n is even

Find the points at which the function f given by f(x)=x^3-3x has local minima and local maxima.

Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimum at x = 3. If p(1) = 6 and p(3) = 2, then p'(0) is

Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 has local maxima local minima point of inflexion

Consider the function f:(-oo,oo)to(-oo,oo) defined by f(x)=(x^2-a)/(x^2+a),a >0, which of the following is not true?(a) maximum value of f is not attained even though f is bounded. (b) f(x) is increasing on (0,oo) and has minimum at x=0 (c) f(x) is decreasing on (-oo,0) and has minimum at x=0. (d) f(x) is increasing on (-oo,oo) and has neither a local maximum nor a local minimum at x=0.