Question

Finding A(x), the area of a rectangle as a function of x, and the maximum value of A(x)?

Answer 1

See explanation.

Explanation:

The sides of the rectangle are `x` and `y`, so the area is:

`A=x*y=x*(20-2x)`

`A=-2x^2+20x`

graph{-2x^2+20x [-118.6, 118.6, -59.4, 59.3]}

From the above graph we see that the function `A(x)` is a parabola with maximum at

`p=(-b)/(2a)=(-20)/-4=5`

The maximum area is:

`A_max=5*(20-10)=50`

Answer:

a) The area is: `A=-2x^2+20x`

b) The maximum area is: `A_max=50`