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Get Full Access to SDSU - MATH 120 - Study Guide - Midterm
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SDSU / Engineering / MATH 120 / How to use the tangent line on the curve?

# How to use the tangent line on the curve? Description

##### Description: I made another version of Gile's Study Guide in case you guys needed any extra practice! I will be posting the answers to this very soon!
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Math 120 – Test 2 Review

## How to use tangent line on the curve?

1. Find the following derivatives:

a. f (x) = 3x4 +7x2 -9x+1 b. f (x)= -(x2 -2)(x2 +6)

c. f (x) = x -3 x2

d. f (x) = x + 2 x -5

## In mathematics, what is the function of horizontal asymptotes?

e. f (x) = x2 -3x +1 f. g(x) = x3 -5 2. Find the slope of the tangent line on the curve f (x) = 6x2 - 3x +3 at the point (3,34)

3. Find the slope of the tangent line on the curve �(�) = &'

'() at the point (-1, 3)

4. Find f’’’(x) and find ‘’’(x) = *

## What is the marginal profit function?

If you want to learn more check out Is cognitive development continuous?

(&'())+

5. A ball is thrown vertically upward with a velocity of 80 ft/sec/ It’s height after t seconds is  given by the function

s(t)= −16�0 + 70.

a) What is the maximum height reached by the ball?

b) What is the velocity when the ball hits the ground?

6. A company that produces and sells jackets determines that the cost of producing x jackets is C  (t)= 0.7�0 − 8� + 300

a) Find the rate at which the cost is changing when 100 jackets are produced.

b) Find the rate at which the average cost is changing when 90 jackets are produced

7. Find the absolute extrema for the following function: �(�) = '7 &'89 on [-3,3] Don't forget about the age old question of What are the strategies to prevent heart disorders?

a. Find the intervals where the function is increasing and/or decreasing.  b. Find all relative extrema.

c. Find the intervals where the function is concave up or concave down.  d. Find any points of inflection. We also discuss several other topics like What forces cause instability in economics?

e. Sketch the graph using the information above.

8. The owner of a surfboard rental company has 14 boards to rent. If he sets the day rental price  at \$10, he can rent 14 cars. For each \$2 increase in the daily rental price, one of the surfboards remains unrented. What daily price will maximize the revenue?Don't forget about the age old question of What is anthropocentric ethics?

9. A store can sell 6 pocket laptops per day at a price of \$130 each. The manager estimated that  that each \$20 price reduction will result in 3 more pocket calculators being sold per day. If each  laptop costs the store \$45, and fixed costs are \$100 per day, find the price that will maximize  profit. Also find the number that will be sold at that price, and the maximum profit.

10. A pet store owner wants to enclose two adjacent rectangular pens of equal size along a  straight wall where the pens will share the common side in the middle. If the sides along the wall  needs no fence, what is the largest area for each pen that can be enclosed using only 400 feet of  fence?

11. A company that produces and sells jackets determines that the cost of producing x jackets is  C (t) = 0.7�0 − 8� + 300 and that the revenue from the sale of x jackets is R(x) = 0.6�0 − 5�. a) Find the marginal profit function.

b) Find and interpret MP (60)

12. Find all vertical and horizontal asymptotes for the following functions:

a) �(�) = '78;

&'7(*

b) �(�) = '(< If you want to learn more check out What are the critical benefits of agriculture?
If you want to learn more check out What are the two hormones involved in human blood glucose regulation?

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