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

Answer:

200 thousands

Step-by-step explanation:

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+200

P(x) = -2(x - 9)² + 200

Differentiating

d(px)/dx  = -2 * 2(x - 9)

=> d(px)/dx  = -4(x - 9)

d(px)/dx  = 0

=> -4(x - 9)  = 0

=> x = 9

d²(px)/dx ² = -4  < 0

=> x = 9 will give maximum value

Maximum number of fish = 200 thousands

Answer 2

Answer:

9

Step-by-step explanation:

KHAN