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?

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