Find the maximum, minimum, and inflection points for the following function ? y = #(x1)^4(x+2)^3#
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To find the maximum, minimum, and inflection points for the function (y = (x1)^4(x+2)^3):
 Maximum and Minimum Points:
 Take the derivative of the function and find critical points by setting it equal to zero.
 Then, use the second derivative test to determine whether these critical points are maxima, minima, or points of inflection.
 Inflection Points:
 Find the second derivative of the function.
 Set the second derivative equal to zero and solve for (x) to find possible inflection points.
 Determine the concavity of the function around these points using the second derivative test.
Let's proceed with the calculations:

First Derivative: (y' = 4(x1)^3(x+2)^3 + 3(x1)^4(x+2)^2)

Critical Points: Set (y' = 0) and solve for (x).

Second Derivative: (y'' = 12(x1)^2(x+2)^3 + 12(x1)^3(x+2)^2 + 6(x1)^4(x+2))

Possible Inflection Points: Set (y'' = 0) and solve for (x).

Evaluate Second Derivative Around Possible Inflection Points: Determine the concavity around these points using the second derivative test.

Final Analysis:
 Identify which critical points correspond to maximum, minimum, or points of inflection.
 Provide the coordinates of these points as the final answer.
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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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