Question

Medal Here!!!

Think of a number less than 20. Subtract this number from 20 and multiply the difference by twice the original number. What is the number that will give the largest product?

Good Luck.

Answer 1

19?

Answer 2

What's next?? Explain please. Thanks.

Answer 3

this is a maxima problem
\[2x(20-x)\]
\[40x-2x^2\]

use first derivative test to find the critical values that will give a candidate for the value of x

\[f \prime= 40-4x\]
\[-4x=-40\]
\[x=\frac{ -40 }{ -4}\]
x=10

use 2nd derivative test to determine if it maximizes or minimizes the value of f(x)

\[f \prime \prime= -4\]
\[f \prime \prime (10) = -4 < 0\]
therefore x=10 maximizes the value of f(x)

x=10 is the number that can give the largest product

2x(20-x)
2(10)(20-10)
200

Answer 4

@Mr.CutieJ you there?

Answer 5

did i get it right ?