# How do you find the local extrema for #f(x)=(x-3)(x-1)(x+2)#?

We need to find the null points of the first derivative of f(x)

hence

this nullifies at points

Using the Second-Derivative Test we have that

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To find the local extrema of ( f(x) = (x-3)(x-1)(x+2) ), you would first find the critical points by setting the derivative equal to zero and solving for ( x ). Then, you would use the first or second derivative test to determine whether each critical point corresponds to a local maximum, local minimum, or neither. The critical points for this function are ( x = -2 ), ( x = 1 ), and ( x = 3 ). You can determine the nature of each critical point by analyzing the behavior of the derivative around each point.

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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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