The two numbers required to solve the following problem are, 13.3 and 6.7
What is Derivative?
The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
Solution:
Let the ture positive numbers be x,(x,y>0)
x + y = 20 -------- Given
We need to maximise [tex]xy^{2}[/tex]
x = 20 - y
f(y) = (20 - y)*[tex]y^{2}[/tex]
f(y) = 20[tex]y^{2}[/tex] - [tex]y^{3}[/tex]
f'(y) = 0
On differentiating:
f'(y) = 40y - 3[tex]y^{2}[/tex]
0 = 40 - 3y
y = 13.3
x = 6.7
To learn more about Derivatives from the given link
https://brainly.com/question/28376218
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