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Refer to Question 16. How fast is the profit increasing when there are only 900 employees (x = 0.9)? Again,round to two decimal places and make sure to include the correct units.Edit View Insert Format Tools TableQuestion 16 is the image

Refer to Question 16. How fast is the profit increasing when there are only 900 employees-example-1

1 Answer

3 votes

Solution

We are given the function


P(x)=ln(4x+1)+3x-x^2

We want to find how fast is the profit increasing when there are only 900 employees (x = 0.9).

To do that, we will have to differentiate P(x) with respect to x and then substitute the value of x = 0.9

Note


\begin{gathered} Given=ln(4x+1) \\ Differentiate=(4)/(4x+1) \\ \\ Given=3x \\ Differentiate=3 \\ \\ Given=x^2 \\ Differentiate=2x \end{gathered}

Now, we differentiate


\begin{gathered} P(x)=ln(4x+1)+3x-x^(2) \\ B\text{y differentiating} \\ P^(\prime)(x)=(4)/(4x+1)+3-2x \\ \\ Pu\text{t x = 0.9} \\ \\ P^(\prime)(0.9)=(4)/(4(0.9)+1)+3-2(0.9) \\ \\ P^(\prime)(0.9)=(238)/(115) \\ \\ P^(\prime)(0.9)=2.069565217 \\ \\ P^(\prime)(0.9)=2.07million\text{ }dollars\text{ }per\text{ }thosandemployees \end{gathered}

Therefore, the answer is


2.07million\text{ }dollars\text{ }per\text{ }thosand\text{ }employees

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