# How do use the first derivative test to determine the local extrema #f(x) = (x+3)(x-4)^2#?

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To use the first derivative test to determine the local extrema of ( f(x) = (x+3)(x-4)^2 ):

- Find the first derivative of the function ( f(x) ) using the product rule.
- Set the first derivative equal to zero and solve for ( x ) to find critical points.
- Test the intervals between the critical points by evaluating the sign of the first derivative within each interval.
- If the sign changes from positive to negative, there is a local maximum; if it changes from negative to positive, there is a local minimum; if there is no sign change, there is neither a local maximum nor a local minimum.

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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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