How many points of inflection does the graph of y=[sin(x)]/x have on the interval (-pi, pi)? 0 1 2 3 4

Question

Is it 2 or 0? What is the answer? Thanks.

Answer 1

Look at a sine curve.

The inflection points are at π/2 and 3π/2.

Answer 2

OK, this problem is a handful and no mistake.

 

You have an inflection point for a function f(x) whenever the second derivative of f(x) = 0. That's where the curvature of the function changes sign.

 

I found the second derivative, and the numerator is what determines zero.

 

(x^2 - 2) sin x + 2x cos x = 0

 

The numerator there has three values of x that make it zero. x=0 and very close to ±2.