`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

Local maximum and local minimum and condition for it

Let f(x)=sinx-x" on"[0,pi//2] find local maximum and local minimum.

For x in (0,(5pi)/2) , define f(x)""=int_0^xsqrt(t)sint"dt" Then f has : local maximum at pi and 2pi . local minimum at pi and 2pi local minimum at pi and local maximum at 2pi . local maximum at pi and local minimum at 2pi .

Let f(x) =x +(1)/(x). find local maximum and local minimum value of f(x) . Can you explain this discrepancy of locally minimum value being greater than locally maximum value.

Let f and g be two differentiable functions defined from R->R^+. If f(x) has a local maximum at x = c and g(x) has a local minimum at x = c, then h(x) = f(x)/g(x) (A) has a local maximum at x = c (B) has a local minimum at x = c (C) is monotonic at x = c 1.a g(x) (D) has a point of inflection at x = c

Which one of the following statements is correct in respect of the function f(x)=x^(3)sin x?(a) It has local maximum at x=0. (b) It has local minimum at x=0. (c) It has neither maximum nor minimum at x=0.( d) It has maximum value 1.

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

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

Find the local maximum and local minimumof f(x)=x^(3)-3x in [-2,4].

Find the points of local maxima and local minima,if any,and local maximum and local minimum values of f(x)=sin x-cos x where ' 0