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Your friend can eat a lot! Cheeseburgers from In-N-Out are his favorite, so he gets happy
when he eats them, that is, until he eats too many! If you measured his happiness, h(x),
based on how many cheeseburgers from In-N-Out he eats, x, you would get a curve modeled
by the function: ℎ() = −12 + 6 + 16....................................................................

Respuesta :

Answer:

There are needed 3 burgers to reach the maximum measure of happiness of 25.

Step-by-step explanation:

The given function is

[tex]h(x)=-x^{2} +6x+16[/tex]

Where [tex]x[/tex] is the number of burgers and [tex]h[/tex] the measure of happiness.

To find the maximum burgers needed to reach the maximum happiness, we just need to find the vertex of this function, which is defined as

[tex]V(h,k)[/tex] where [tex]h=-\frac{b}{2a}[/tex], and [tex]b=6[/tex], [tex]a=-1[/tex], replacing these values, we have

[tex]h=-\frac{6}{2(-1)}=3[/tex]

[tex]k=f(3)=-(3)^{2} +6(3)+16=-9+18+16=25[/tex]

Therefore, there are needed 3 burgers to reach the maximum measure of happiness of 25.

fichoh

Using the maximum function relation, the maximum number of cheeseburgers to be consumed would be 25

Given the function :

  • h(x) = - x² + 6x + 16

The function is maximum at [tex] \frac-{b}{2a}[/tex]

b = 6 ; a = - 1

Hence, we have :

[tex] x = \frac-{6}{2(-1)} = 3 [/tex]

Substitute x = - 3 into the function :

h(-3) = - (3)² + 6(3) + 16

h = - 9 + 18 + 16

h = 25

Therefore, the maximum number of cheeseburgers to be tanken would be 25

Learn more : https://brainly.com/question/25589810

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