Answer to Question #256718 in Calculus for junior

Question

Consider a rectangle with perimeter 28 (units). Let the width of the rectangle be w (units) and let the Area of the region enclosed by the rectangle be A ( square units). Express A as a function of w and state the domain and range of the function.

Answer 1

the width of the rectangle:

$l=(28-2w)/2$

$A=wl=w(28-2w)/2=14w-w^2$

domain: $w\isin (0,14)$

$A'(w)=14-2w=0$

$A_{max}=A(7)=14\cdot7- 7^2=49$

range: $A\isin (0,49]$