# What are the critical points of #f(x) =2e^(3x)-3xe^(2x)#?

To compute critical points of a function, you need its first derivative.

We need two rules: first of all, the derivative doesn't care about multiplicative factors, so

The chain rule states that

Which in your case becomes

In addition to what we saw before, we need to add the rule for deriving a product of two functions, which is

So, we have that

Finally, sum up the two pieces: we have

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The critical points of f(x) = 2e^(3x) - 3xe^(2x) are found by setting the derivative equal to zero and solving for x. The derivative of f(x) with respect to x is f'(x) = 6e^(3x) - 3e^(2x) - 6xe^(2x). Setting f'(x) equal to zero and solving for x yields the critical points.

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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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