How does the first derivative test work?

Answer 1
First Derivative Test for Local Extrema Let #x=c# be a critical value of #f(x)#. If #f'(x)# changes its sign from + to - around #x=c#, then #f(c)# is a local maximum. If #f'(x)# changes its sign from - to + around #x=c#, then #f(c)# is a local minimum. If #f'(x)# does not change its sign around #x=c#, then #f(c)# is neither a local maximum nor a local minimum.
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Answer 2

The first derivative test is a method used to analyze critical points of a function to determine whether they correspond to local maxima, local minima, or saddle points. The test relies on the behavior of the function's derivative in the vicinity of these critical points. Specifically, if the derivative changes sign at a critical point from positive to negative, the point corresponds to a local maximum. If the derivative changes sign from negative to positive, the point corresponds to a local minimum. If the derivative does not change sign at the critical point, it indicates a saddle point.

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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.

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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