The max of these functions?

Question

1) A(w) = 20w - 1.285 w^2

2) A(w) = 20w - 1.57w^2

3) A(w) = 20w - 1.5 w^2

4) A(w) = 20w - 2w^2

Answer 1

Are you doing pre-calc? Easy to solve with simple derivative... see reference for to good tutorial. Max is reached when 1st derivative is zero.

dw(A(w)) = 0

1st one:
20 - 2*1.285w = 0
w = 20/2*1.285
w = 7.78

Answer 2

The maximum is the first equation.

Since w^2 is always greater than zero, we can see that the smaller the coefficient of w^2, the larger the function.

Is that what the question means, or are you looking for the maximum value of each function? To do this, find the derivative. For the first, it is 20-1.285*2w, or w = 10/1.285

Answer 3

1) A(w) = 20w - 1.285 w^2
dA/dw=20-2.47w=0
w=20/2.47
2) A(w) = 20w - 1.57w^2
dA/dw=20-3.14w=0
w=20/3.14
3) A(w) = 20w - 1.5 w^2
dA/dw=20-3w=0
w=20/3
4) A(w) = 20w - 2w^2
dA/dw=20-4w=0
w=20/4=5

substitute the values of w obtained to get the max value of the functions

Answer 4

well I'm not sure what level of math you're at. If you're in calculus find the derivative of the function, then find where the derivative equals zero and then make a chart to figure out whether each of those points is a max or a min.


If you have no clue what a derivative is, i guess I would suggest graphing on a graphing calculator. Or by hand.