Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
Find the x-coordinate of the point on the curve y= x that is closest to the point (4,0).
- 4
- 3.5
- 2
- 3
Answer
B. 3.5
Solution
The squared distance is D=(x-4)2+( x)2=(x-4)2+x. D'=2(x-4)+1=0 x=3.5.
More Optimization (Maxima and Minima) questions
- Find two positive numbers whose sum is 20 and whose product is a maximum.
- A farmer has 200 m of fencing to enclose a rectangular field bordered on one side by a river (no fence is needed along the river). Find…
- An open-top box is made by cutting equal squares of side x from each corner of a 12 in by 12 in sheet of cardboard and folding up the…
- A rectangular box with a square base and no top is to have a total surface area of 108 square inches. Find the maximum possible volume.
- A closed cylindrical can is to have a volume of 16π cubic inches. Find the radius that minimizes the total surface area.
- Find the point on the line y=2x+3 that is closest to the origin.
- A right circular cylinder is inscribed in a sphere of radius 6. Find the height of the cylinder that maximizes its volume.
- A wire 100 cm long is cut into two pieces. One piece is bent into a square and the other into a circle. How many centimeters of wire…
- An open rectangular box with a square base is to have a volume of 32 cubic feet. Find the dimensions that minimize the amount of material…
- A Norman window (a rectangle surmounted by a semicircle) is to have a perimeter of 20 ft. Find the radius of the semicircle that maximizes…