What symmetries if any does fx Square root 4 x2 have Is th

What symmetries (if any) does f(x) = Square root 4 - x^2 have? Is the function even, odd, or neither? A car dealership has 24ft of dividers with which to enclose a rectangular play space in a corner of a customer lounge. The sides against the wall require no partition. Suppose the play space is x feet long. (Draw a picture). Express the area of the play space as a function of x. Find the domain of the function. Use the graph to determine the dimensions that yield the max area.

Solution

5)

f(x) = sqrt( 4 - x^2 )

to check even or odd symmetry , plug x=-x in f(x)

f(-x) = sqrt( 4 - (-x)^2 )

f(-x) = sqrt(4 - x^2)

f(-x) = f(x)

so this is an even symmetric function

6).

Area of rectangle = length* breadth

so

Area (A) = x*(24 - x) = x² - 24x



Domain: Probably 0 -- 144 ft²

dA/dx = 2x - 24 = 0 [x = 12, y = 12] for Amax