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

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#