Find the most general antiderivative of the function. (Check your answer by differentiation.)

$$f(x) = 2√x+6cosx$$

The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is $800 per month. A market survey suggests that, on average, one additional unit will remain vacant for each$10 increase in rent. What rent should the manager charge to maximize revenue?

The manager of a 100-unit apartment complex knows from experience that all units will be occupied if the rent is per month. A market survey suggests that, on average, one additional unit will remain vacant for each $10 increase in rent. What rent should the manager charge to maximize revenue?

A boat leaves a dock at 2:00 PM and travels due south at a speed of 20 km / h. Another boat has been heading due east at 15km / h and reaches the same dock at 3:00 PM. At what time were the two boats closest together?

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent intoother into a circle. How should the wire be cut so that the total area enclosed is (a) a maximum? (b) A minimum?

A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a minimum?

A piece of wire 10 meters long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is a minimum?

A piece of wire 10 meters long is cut into two pieces. One piece is bent into a square and the other into a circle. How should the wire be cut so that the total area enclosed is a minimum?

A rectangular storage container with an open top is to have a volume of 10 m$^3$ . The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs$6 per square meter. Find the cost of materials for the cheapest such container.

If 1200 $cm^2$ of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

What is the maximum vertical distance between the line y=x+2 and the parabola y=x^2 for -1<=x<=2?

Find the local maximum and minimum values of f using both the First and Second Derivative Tests. Which method do you prefer? f(x) = √x - 4√x

Given that, lim x to a f(x)=0, lim x to a g(x)=0, lim x to a h(x)=1, lim x to a p(x)=infinite, lim x to a f(x)=infinite. Is the following limit indeterminate forms? For this that is not an indeterminate form, evaluate the limit where possible. lim x to a h(x)/p(x)

Find the local maximum and minimum values of f, f(x)=sinx+cosx, 0<=x<=2pi