Question

Find the point of diminishing returns (x comma y )for the function​ R(x), where​ R(x) represents revenue​ (in thousands of​ dollars) and x represents the amount spent on advertising​ (in thousands of​ dollars).

Answer 1

Complete Question

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Answer:

The point of diminishing returns (x , y ) is  (11, 21462)

Step-by-step explanation:

From the question we are told that

     The function is  $R(x) = 10,000 -x^3 - 33x^2 + 800x , \ \ 0 \le x \le 20$

Here R(x)  represents revenue (in thousands of​ dollars) and  x  represents the amount spent on advertising​ (in thousands of​ dollars).

           Now  differentiating  R(x) we have  

               $R'(x) = -3x^2 +66x + 800$

Finding the second derivative of R(x)

              $R''(x) = -6x +66$

at  inflection point    $R''(x) = 0$

    So      $-6x +66 = 0$

=>           $x= 11$

    substituting value of x into R(x)

     $R(x) = 10,000 -(11)^3 - 33(11)^2 + 800(11) ,$

      $R(x) = 21462$

Now the point of diminishing returns (x , y ) i.e (x , R(x) ) is

     (11, 21462)