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Leona [35]
3 years ago
9

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=−2. The y-intercept is y

=−9.6 . Find a formula for P(x) . Keep the answer in factored form.
Mathematics
1 answer:
Sedbober [7]3 years ago
8 0

Answer:

Step-by-step explanation:

P(x) = a(x - 2)2(x + 4), a ≠ 0

 

Use the given point (0,-10) to find a.

 

-10 = a(0 - 2)2(0 + 5) = a(4)(5) = 20a

a = -10/20 = -1/2

 

P(x) = (-1/2)(x - 2)2(x + 5)

 

You can expand this if you wish

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Find the point of diminishing returns (x comma y )for the function​ R(x), where​ R(x) represents revenue​ (in thousands of​ doll
riadik2000 [5.3K]

Complete Question

The complete question is shown on the first uploaded image  

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)

4 0
3 years ago
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