# Given #f(x) = -2(x+2)(x-1)^2# on the open interval (-3,3). How do you determine the x coordinate of the relative minimum of f (x) in the open interval (-3,3)?

Relative minimum at

Start by differentiating. Since we're not dealing with too high powers, it would be easiest to expand.

We now differentiate using the power rule.

We must now test the sign of the derivative on both sides of these points.

Hopefully this helps!

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To determine the x-coordinate of the relative minimum of ( f(x) ) in the open interval (-3, 3), follow these steps:

- Find the critical points of ( f(x) ) within the interval (-3, 3) by setting the derivative of ( f(x) ) equal to zero and solving for ( x ).
- Evaluate the second derivative of ( f(x) ) at each critical point.
- Identify the critical points where the second derivative is positive, indicating a relative minimum.
- Check if the critical points found in step 3 fall within the interval (-3, 3).
- Determine the x-coordinate of the relative minimum among the critical points identified in step 4.

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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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