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the graph of y=f"(x) for a function f is shown. number of points of inflection for y=f(x)

the graph of y=f"(x) for a function f is shown. number of points of inflection for y=f(x)

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Grade:12

2 Answers

Aditya Gupta
2081 Points
4 years ago
 A necessary condition for  to be an inflection point is f”(x)=0. A sufficient condition requires f”(x+e) and f”(x – e) to have opposite signs in the neighbourhood of x.
here, obviously f”(x)=0 at A, C and E.
however, the sign of f”(x) in any neighbourhood however small around the point C is positive and doesnt change.
so, number of points of inflection for y=f(x) is 2 (A and E).
kindly approve :)
Sambhav
15 Points
4 years ago
you can simply answer this question by seeing the graph....
point of inflection is a point where a graph change its curvature, in graph there are two points where the graph change its curvature i.e.  at B and D.

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