Exam 2

Question 1

Chain rule

Answer 1

g(h(x)) h’(x)

Question 2

Approximation by Increments formula

Answer 2

Δf = f’(x) Δx

Question 3

What keywords tell you to use the approximation formula?

Answer 3

marginal, estimate

Question 4

How do you do implicit differentiation?

Answer 4

1.) Take derivative and “fly the flag” with y’ wherever y occurs
2.) Get y’ on one side

Question 5

What to do given the skilled labor problem?

Answer 5

1.) Take derivative using Δx and Δy
2.) Get Δy on one side
3.) Plug in values

Question 6

How do you find critical numbers?

Answer 6

Set first derivative = 0

Question 7

How can you find where the function is increasing/decreasing?

Answer 7

Use sign diagram

Question 8

How can you find the points where max/mins are?

Answer 8

( critical point f’, f(critical point f’))

Question 9

How can you determine where a function is concave up/down?

Answer 9

1.) Set second derivative = 0
2.) Use sign diagram to find where f’’ is concave up/down

Question 10

How do you get inflection points?

Answer 10

(critical value f’’, f(critical value f’’))

Question 11

If x = c is a critical value of f and f’‘(c) < 0, then x = c is a local min of f
True
False

Answer 11

False

Question 12

Second derivative test

Answer 12

1.) Get zeros of f(x)
2.) Plug into second derivative

If f’‘(c) < 0 concave down, max
If f’‘(c) > 0 concave up, min

Question 13

How do you get Horizontal Asymptote and Vertical Asymptote?

Answer 13

HA: ratio of leading coefficients (if degree is same)
VA: set denom = 0

Question 14

How do you get the x and y intercepts?

Answer 14

x int: numerator = 0
y int: set function = 0

Question 15

What do the first and second derivative mean in the context of efficiency?

Answer 15

First: efficiency
Second: how efficiency is changing

Question 16

Marginal vs Actual Cost

Answer 16

Marginal: use approximation formula
Actual: do C(21) - C(20)