Question

The fish population in a certain part of the ocean (in thousands of fish) as a function of the water's temperature (in degrees celsius) is modeled by: p(x)=-2(x-9)^2+200p(x)=−2(x−9) 2 +200p, left parenthesis, x, right parenthesis, equals, minus, 2, left parenthesis, x, minus, 9, right parenthesis, start superscript, 2, end superscript, plus, 200 what is the maximum number of fish?

Answer 1

We have the following function:
 p (x) = - 2 (x-9) ^ 2 +200
 We derive to find the maximum of the function:
 p '(x) = - 4 (x-9)
 Rewriting:
 p '(x) = - 4x + 36
 We match zero:
 -4x + 36 = 0
 We clear x
 x = 36/4
 x = 9 degrees
 The maximum population occurs when x = 9.
 We evaluate the function for this value:
 p (9) = - 2 * (9-9) ^ 2 +200
 p (9) = 200
 Answer:
 The maximum number of fish is:
 p (9) = 200

Answer 2

Answer: 9 degrees Celsius

Step-by-step explanation: it says it on Khan Academy