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The second derivative of a function f is given by f " (x) = xsinx - 2.

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How many points of inflection does f have on the interval (-10,10)? 

the options are 


asked Oct 4, 2014 in PRECALCULUS by anonymous

1 Answer

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The second derivative of function is f " (x) = x * sin(x) - 2.

Points of Inflection : If (c, f(c)) is a point of inflection of the graph of f(x), then either f " (c) = 0 or f " (x) does not exist at x = c.

Graph for f " (x) = x * sin(x) - 2 :

Observe the graph, the graph crosses the x-axis at four places, so the number of points of inflection of the graph of f(x) is four in the interval (-10, 10).

The option C is correct.

answered Oct 4, 2014 by casacop Expert

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