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

There is a point of inflection whenever

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

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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To find all points of inflection for the function ( y = -2 \sin(x) ), you need to locate where the second derivative changes sign.

First, find the first derivative of ( y ) with respect to ( x ), then find the second derivative. Set the second derivative equal to zero and solve for ( x ) to find critical points. Next, determine the intervals where the second derivative changes sign by testing points in each interval.

The points where the second derivative changes sign correspond to points of inflection for the function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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