How do you find all points of inflection given y=-2sinxy=−2sinx?

1 Answer
Katherine H.
Jun 21, 2017

There is a point of inflection whenever -2sinx=0−2sinx=0

Explanation:

Points of inflection occur when the curve changes concavity. Since this is a sine wave, there are an infinite number of points of inflection.

A function is concave up when the second derivative (f'') is greater than 0, and concave down when the second derivative is below 0. Critical points, therefore, are when the second derivative equals 0.

Differentiate y=-2sinx to get y'=-2cosx. Differentiate again to get y''=2sinx, the original function.

Whenever -2sinx=0, there is a point of inflection. This can be intuitively verified by graphing y=-2sinx.

graph{-2sinx [-pi, pi, -3, 3]}

Whenever the curve crosses the x-axis (that is, whenever y=0), the concavity changes.

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