# How do you find the inflection point(s) of the following equation #(1+ln(x))^3#?

I'm going to assume that you are generally aware of how to locate inflection points.

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To find the inflection point(s) of the equation (1+ln(x))^3, we need to find the second derivative and then solve for the points where it equals zero.

First, differentiate (1+ln(x))^3 with respect to x:

d/dx [(1+ln(x))^3]

= 3(1+ln(x))^2 * d/dx [1+ln(x)]

= 3(1+ln(x))^2 * (1/x)

Now, take the second derivative:

d^2/dx^2 [(1+ln(x))^3]

= d/dx [3(1+ln(x))^2 * (1/x)]

= d/dx [3(1+ln(x))^2 * (1/x)]

= 3 * d/dx [(1+ln(x))^2 * (1/x)]

= 3 * [(d/dx [(1+ln(x))^2] * (1/x)) + ((1+ln(x))^2 * d/dx [1/x])]

= 3 * [(2(1+ln(x)) * (1/x) * (1/x)) + ((1+ln(x))^2 * (-1/x^2))]

= 3 * [2(1+ln(x))/x^2 - (1+ln(x))^2/x^2]

Now, set this expression equal to zero and solve for x:

3 * [2(1+ln(x))/x^2 - (1+ln(x))^2/x^2] = 0

2(1+ln(x)) - (1+ln(x))^2 = 0

Now, solve this equation for x to find the inflection point(s).

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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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