Let `I RvecI R` be defined as `f(x)=|x|+|x^2-1|dot` The total number of points at which `f` attains either a local maximum or a local minimum is_______

Find the local maximum and local minimum of f(x) = 2x^(3) + 5x^(2) - 4x

Let f:RtoR be defined by f(x)=x/(1+x^2),x inR . Then the range of f is

Let f be a function defined on R (the set of all real numbers) such that f^(prime)(x)=2010(x-2009)(x-2010)^2(x-2011)^3(x-2012)^4, for all x in Rdot If g is a function defined on R with values in the interval (0,oo) such that f(x)=ln(g(x)), for all x in R , then the number of point is R at which g has a local maximum is ___

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 function defined as follows: f(x)=sin(x^2-3x),xlt=0; a n d6x+5x^2,x >0 Then at x=0,f(x) has a local maximum has a local minimum is discontinuous (d) none of these

Let f(x) = max. {|x^2 - 2| x ||,| x |} then number of points where f(x) is non derivable, is :

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

Let f(X) be real valued continous funcion on R defined as f(X) = x^(2)e^(-|x|) Number of points of inflection for y = f(X) is

Let a function f be defined by f(x)=(x-|x|)/x for x ne 0 and f(0)=2. Then f is