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=-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.


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.


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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