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A company is using the first two years of its profits to predict what will happen in the future. The profit, p(x), in millions, can be modeled by
the function p(x) =x^2 + 4x + 5, where x, represents the number of years after 2020



- In what year did the company have the largest profit and what was the amount?

Respuesta :

semsee45

Answer:

2022

9 million

Step-by-step explanation:

[tex]p(x) =-x^2 + 4x + 5[/tex]

To find the value of x when the maximum profit occurs, differentiate the function:

[tex]\implies p'(x)=-2x+4[/tex]

set it to zero and solve for x:

[tex]\implies p'(x)=0[/tex]

[tex]\implies -2x+4=0[/tex]

[tex]\implies x=2[/tex]

Therefore, the year in which the company had its largest profit was

2020 + 2 = 2022

Input found value of x into the function:

[tex]p(2) =-(2)^2 + 4(2) + 5=9[/tex]

Therefore, the amount was 9 million

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