Advanced Applications

Question 1

What’s the product rule?

Answer 1

(𝐹𝑆)′ =𝐹′𝑆+𝐹𝑆′

Question 2

Express x^5 as a product of five things.

Answer 2

𝑥⋅𝑥⋅𝑥⋅𝑥⋅𝑥

Question 3

Express 2xyz as a product of two things.

Answer 3

(2x)(yz)

Question 4

What is (45^3 * 32^80)′

Answer 4

0

Question 5

What is lim Δ𝐴/Δ𝑥?
Δ𝑥→0

Answer 5

A’

Question 6

What is lim Δ(𝐴^2 * 𝐵)/Δ𝑥 ?
Δ𝑥→0

Answer 6

(𝐴^2 * 𝐵)′

Question 7

What is lim Δ𝐴⋅Δ𝐵/Δ𝑥 ?
Δ𝑥→0

Answer 7

0

Question 8

Changes from increasing to decreasing can only occur at what__________.

Answer 8

critical points

Question 9

If the only critical points are x = 2, 7 and 11 and 𝑓′(9) =
5, what do we know about a region of the graph?

Answer 9

It’s increasing between 7 and 11. Because the 5 is positive

Question 10

Who is the mathematician who discovered the
importance of critical points?

Answer 10

Fermat

Question 11

What’s the quotient rule?

Answer 11

T/𝐵 = 𝑇′𝐵−𝑇𝐵′
__________
B^2

Question 12

How do we know the T’ term in the quotient rule is
positive?

Answer 12

When the top of a fraction grows, the fraction grows.

Question 13

How do we know the B’ term in the quotient rule is
negative?

Answer 13

When the bottom of a fraction grows, the fractions
shrinks.

Question 14

What are the three places where extreme function values can occur?

Answer 14

F’ = 0, F’ DNE, End Points

Question 15

Which of the three are “critical points”

Answer 15

F’ = 0, F’ DNE,

Question 16

(g(f(x)))′ = ____________________

Answer 16

𝑔′(𝑓(𝑥))𝑓′(𝑥)

Question 17

Intuitively what is 𝑑𝐸𝑔𝑔𝑠/𝑑𝐶𝑎𝑟𝑡𝑜𝑛𝑠?

Answer 17

Eggs per Carton

Question 18

Express miles per gallon twice, using both derivative
notations.

Answer 18

Miles′(Gallon), 𝑑𝑀𝑖𝑙𝑒𝑠/𝑑𝐺𝑎𝑙𝑙𝑜𝑛𝑠

Question 19

Rad(Deg) turns degrees into radians. What is the
expression for this function?

Answer 19

𝑅𝑎𝑑(𝐷𝑒𝑔)= 𝜋/180 (𝐷𝑒𝑔)

Question 20

Write COS(x) in terms of cos(x).

Answer 20

𝐶𝑂𝑆(𝑥)=cos( 𝜋/180𝑥)