If sign of f'(x) doesn't change at `x_(0),`
while moving from left to right, then f(x) has neither a maximum nor a minimum at `x_(0).`

Prove that,function x^(3)-3x^(2)+3x+7 neither has maximum nor minimum at x=1

If f(x)=|x|+|x-1|+|x-2| then which one of the following is not correct? (A) f(x) has a minimum at x=1 (B) f(x) has a minimum at x=0 (C) f(x) has neither a maximum nor a minimum at x=0 (D) f(x) has neither a maximum nor a minimum at x=2

If f'(x) changes from negative to positive at x_(0) while moving from left to right, i.e. f'(x)lt0,xltx_(0) f'(x)gt0,xgtx_(0), then f(x) has local minimum value at x=x_(0)

Write True/False: If f'( c )=0 then f(x) has a local maximum or a local minimum at x=c

Show that the function x^(5)-5x^(4)+5x^(3)-10 is neither maximum nor minimum at x=0

If f'(x) changes from positive to negative at x_(0) while moving from left to right, i.e. f'(x)gt0,xltx_(0) f'(x)lt0,xgtx_(0), then f(x)has local maximum value at x=x_(0)

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.

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+(1)/(x),xne0. Discuss the maximum and minimum value of f(x).