4.7 Homework - Optimization (Homework)

1. [-/1 Points] DETAILS SCALCET9 4.7.002.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find two numbers whose difference is 82 and whose product is a minimum. smaller number larger number Need Help? Read It Master It 2. [-/1 Points] DETAILS SCALCET9 4.7.005.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a function that gives the vertical distance v between the line y = x + 42 and the parabola y = x2 for -6 s x $ 7. V ( x ) = Find v'(x). v' ( x ) = What is the maximum vertical distance between the line y = x + 42 and the parabola y = x2 for -6 s x $ 7? Need Help? Read It3. [-/1 Points] DETAILS SCALCET9 4.7.007.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the dimensions of a rectangle (in m) with perimeter 60 m whose area is as large as possible. (Enter the dimensions as a comma-separated list.) Need Help? Read It Watch It Master It 4. [-/1 Points] DETAILS SCALCET9 4.7.013.EP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence. Let F represent the length of fencing in feet. Write an equation that represents F in terms of the variable x. F ( x ) = Find the derivative F'(x). F' ( X) = Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value Ift Need Help? Read It5. [-/1 Points] DETAILS SCALCET9 4.7.029. MY NOTES ASK YOUR TEACHER Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. width units height units Need Help? Read It Watch It