Monday
April 21, 2014

Homework Help: CALCULUS - Check my answers :)

Posted by Samantha on Thursday, December 19, 2013 at 7:18pm.

I'd appreciate corrections for the ones I get wrong. :) Thanks!

1. Determine which of the following is true for the function f(x) = x^3 +5x^2 - 8x +3.
I. f(x) has a relative minimum at x = 2/3.

II. f(x) has a relative maximum at x = 2/3.

III. f(x) has a zero at x = 2/3

I only
*II only
III only
I and III only
II and III only

2. Determine the equation of the normal line to y = x^2 + 5 at the point (2, 9)

y=-1/4x + 17/4
*y=1/2x + 8
y=4x+1
y=4x-34
y=-1/4x + 19/2

3. If 12 ft^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.

2 ft^3
4 ft^3
5 ft^3
*8.5 ft^3
9 ft^3

4. Find the tangent line approximation, L(x), of f(x)=x^2/3 at x = 8.
L(x) = 4/3x-20/3
L(x) = 2/3x+8
L(x) = 4(x-8)
L(x) = 1/3x + 4/3
*L(x) = 4/3x - 8/3

5. A balloon is rising at a constant speed of 5 ft/sec. A boy is cycling along a straight road at a constant speed of 15 ft/sec. When he passes under the balloon, it is 5 feet above him. Approximately how fast is the distance between the boy and the balloon increasing 3 seconds after he has passed underneath it?
12 ft/sec
16 ft/sec
20 ft/sec
*25 ft/sec
30 ft/sec

6. A factory is manufacturing a rectangular storage container with an open top. The volume of the container is 10 ft^3, and the length of the base is twice the width. The material for the base costs $10 per square foot, and the material for the sides costs $6 per square foot. Find the cheapest cost to make the container, given the conditions.

$27.85
$46.19
*$87.24
$147.85
$163.54


7. The edge of a cube was found to have a length of 50 cm with a possible error in measurement of 0.1 cm. Based on the measurement, you determine that the volume is 125,000 cm^3. Use tangent line approximation to estimate the percentage error in volume.

0.6%
0.9%
*1.2%
1.5%
1.8%

8. An inverted conical tank (with vertex down) is 14 feet across the top and 24 feet deep. If water is flowing in at a rate of 12 ft^3/min, find the rate of change of the depth of the water when the water is 10 feet deep.

0.007 ft/min
0.449 ft/min
0.018 ft/min
*0.051 ft/min
0.065 ft/min


9. For the function f(x)=Inx/x^2, find the approximate location of the critical point in the interval (0, 5).

(0.5, −2.773)
(1, 0)
(1.649, 0.184)
*(2, 0.173)
(0.778, −1.813)

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