`Let f(x)={(|x|,for 0<|x|lt=2), (1,"for"x=0):}` Then at `x=0,f(x) has
(a) a local maximum
(b) no local maximum
(c) a local minimum
(d) no extremum

Let h(x)=x^(m/n) for x in R , where +m and n are odd numbers and 0 less than m less than n Then y=h(x) has a)no local extremums b)one local maximum c)one local minimum d)none of these

Lert f:[a , b]vec be a function such that for c in (a , b),f^(prime)(c)=f^"(c)=f^"'(c)=f^(i v)(c)=f^v(c)=0. Then f (a)has a local extermum at x=c dot (b) f has neither local maximum nor minimum at x=c (c) f is necessarily a constant function (d)it is difficult to say whether (a)or(b)dot

Let the function f(x be defined as follows: f(x)={x^3+x^2-10 x ,-1lt=x<0cosx ,0lt=x

L e tf(x)={((x-1)(6x-1))/(2x-1),ifx!=1/2 0,ifx=1/2 Then at x=1/2, which of the following is/are not true? (a) f has a local maxima (b) f has a local minima (c) f has an inflection point. (d) f has a removable discontinuity.

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

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

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

The function f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a local maximum at x equal to: