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A point c in the domain of a function f(x) is said to be critical if ,the value of its first derivative at that point f’(c)=0.

Further (a)  If f’(x) changes sign from positive to negative as x increase through c, then c is said to be                              a point of local maximum.

(b)  If f’(x) changes sign from negative  to positive as x increase through c,then c is said to be a point of local minimum.

(c) If f’(x) does not change sign ,as x increases through c, then c is said to be a point of inflection..

In the present case f(x)= x^3. Therefore   f’(x) =  3 x^2 . By putting f”(x) =3 x^2 = 0 ,we get the

critical point c= 0. It can be seen that f’(x) does not change sign and remains positive as  x

increases through 0{ because f’(x) positive for both negative and positive values of x}.

Hence x= 0 , is a point of inflexion. Moreover x=10 is not a point of inflexion as f'’(10) is not equal to zero ,when x =10.    

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For the point of inflection, you have to know the concept of derivative firstly

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