# 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?

##### 1 Answer

Jun 15, 2018

At 5,000 units, the absolute maximum profit is

#### Explanation:

**1st derivative to optimise** :

**2nd derivative test for max/min** :

#{(P''(1) = 12 > 0),(P''(5) = - 12 < 0):}#

So profit is maximised at

That is, at 5,000 units, the profit is