A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section)of 168 inches. Write a function that represents the volume of the package. A)V(x)= - 4x²(42 + x) B)V(x)= 4x²(42 + x) C)V(x)= 4x²(42 - x) D)V(x)= 4x²(-42 - x) E)V(x)= - 4x²(42 - x)

Question

Quizplus · Accepted Answer

The formula for the volume of a rectangular box is V(x) = (length) × (width) × (height) = x(42 − 2x) × (x). We can simplify this to V(x) = 2x^2 (42 − x). To maximize the volume, we need to find the value of x that gives us the maximum value of V(x). We can do this by taking the derivative of V(x) and setting it equal to 0: V'(x) = 84x − 4x^2 = 0. Solving for x, we get x = 21. Substituting x = 21 back into our formula for V(x), we get V(21) = 2(21)^2 (42 − 21) = 882 cubic inches. Therefore, the function that represents the volume of the package is V(x) = 2x^2 (42 − x), which corresponds to choice C.

A Rectangular Package to Be Sent by a Delivery Service