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

Question

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

the options are 
a)zero 
b)two 
c)four 
d)six 
e)eight

 

Answer 1

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.