# Can some one help with this one? I am new to derivatives.

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A company finds that the profit 𝑃(𝑥) where 𝑥 represents thousands of units, is given by

𝑃(𝑥)=#−x^3+9x^2−15x−9#

If the company can only make a maximum of 6000 units, what is the absolute maximum profit?

A company finds that the profit 𝑃(𝑥) where 𝑥 represents thousands of units, is given by

𝑃(𝑥)=

If the company can only make a maximum of 6000 units, what is the absolute maximum profit?

At 5,000 units, the absolute maximum profit is

1st derivative to optimise :

2nd derivative test for max/min :

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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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