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How do you determine the concavity of # y=2cosx+sin2x#?

Answer 1

Charles Arocha

This function is periodic. Concavity should also be periodic and meaningless

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Answer 2

Luke Alvarez

To determine the concavity of ( y = 2 \cos(x) + \sin(2x) ), you need to find the second derivative of the function and then examine its sign. If the second derivative is positive, the function is concave up, if negative, it's concave down, and if zero, there is an inflection point.

First, find the first derivative of the function: [ \frac{dy}{dx} = -2\sin(x) + 2\cos(2x) ]

Next, find the second derivative: [ \frac{d^2y}{dx^2} = -2\cos(x) - 4\sin(2x) ]

Now, examine the sign of the second derivative to determine concavity.

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Answer from HIX Tutor

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.