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1-Find the point on the line 5 x + 7 y - 4 =0 which is closest to the point ( -2, -4 ) .

2-A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 9-x^2 . What are the dimensions of such a rectangle with the greatest possible area?

Width = Height =

3-An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

Dimensions of the bottom of the box: x Height of the box:

4-A javalina rancher wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). He has 690 feet of fencing available to complete the job. What is the largest possible total area of the four pens?

Note: you can click on the image to get a enlarged view.

Largest area = $\textrm{ft}^2$

5-A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 4.5. What are the dimensions of such a cylinder which has maximum volume?

Radius = Height =

6-A car rental agency rents 180 cars per day at a rate of 26 dollars per day. For each 1 dollar increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income, and what is the maximum income? Rate = Maximum Income =

7-Find the positive number that minimizes the sum of itself plus 8 times its reciprocal.

Answer:

8-A gardener wants to choose a rectangular region of 3100 square feet of land so that when she surrounds the the region with edging and divides the region in half with additional edging parallel to two of the sides of the region, she minimizes the total amount of edging used. Find this minimum total amount of edging.

Answer: feet

9-Consider the function f(x) = 32 x^3 - 21 x^2 + 14 x - 7 . Enter an antiderivative of f(x)

10-Consider the function $f(t) = 7 \sec ^2(t) - 3 t^ { 3 }$ . Let F(t) be the antiderivative of f(t) with F(0) = 0 . Then F(t) equals

11-Consider the function $\displaystyle f(x) = \frac { 4 }{ x^ {3} } - \frac { 4 }{ x^ { 5 }}$ . Let F(x) be the antiderivative of f(x) with F(1) = 0 . Then F(x) =

12-A particle is moving with acceleration a(t) = 24 t + 18 . its position at time t =0 is s(0) = 13 and its velocity at time t =0 is v(0) = 9 . What is its position at time t = 5 ?

13-A stone is thrown straight up from the edge of a roof, 825 feet above the ground, at a speed of 16 feet per second. A. Remembering that the acceleration due to gravity is -32 feet per second squared, how high is the stone 5 seconds later? B. At what time does the stone hit the ground? C. What is the velocity of the stone when it hits the ground?

14-Find the antiderivative, G(x) , of the function: $g(x)=\frac{5-4 x^3+2 x^6}{x^6}$ if G(1)=0 G(x)=