How do you find points of inflection for #y= sin x + cos x#?
The point of inflexion are:
 We must first determine our function's second derivative.
Two cases need to be handled by us.
Case 1
Case 2
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To find the points of inflection for ( y = \sin(x) + \cos(x) ), we need to find where the second derivative changes sign.

First, find the first derivative of ( y ) with respect to ( x ), which is ( y' = \cos(x)  \sin(x) ).

Next, find the second derivative of ( y ) with respect to ( x ), which is ( y'' = \sin(x)  \cos(x) ).

Set ( y'' ) equal to zero and solve for ( x ) to find the critical points.
[ \sin(x)  \cos(x) = 0 ]
[ \sin(x) + \cos(x) = 0 ]
 Solve for ( x ) by applying trigonometric identities or graphical methods.
[ \sin(x) = \cos(x) ]
[ \tan(x) = 1 ]
[ x = \frac{3\pi}{4} + n\pi, \quad \text{where } n \text{ is an integer}]

Once you have the critical points, test the sign of the second derivative on intervals determined by these critical points to determine where the concavity changes.

The points where the concavity changes from concave up to concave down, or vice versa, are the points of inflection.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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