Question -
Answer -
Let one number be x. Then, theother number is y = (35 − x).
Let P(x) = x2y5. Then, we have:
x =0, x = 35, x = 10
When x =35,
and y = 35 − 35 = 0.This will make the product x2 y5 equalto 0.
When x = 0, y =35 − 0 = 35 and the product x2y2 willbe 0.
∴ x = 0 and x = 35 cannotbe the possible values of x.
When x = 10, we have:
∴ By second derivative test, P(x) willbe the maximum when x = 10 and y = 35 − 10 =25.
Hence, the required numbers are 10 and 25.