Test 2

Question 1

Product Rule:

Answer 1

f’xgx + g’xfx

Question 2

Quotient Rule:

Answer 2

(gxf’x - fxg’x) / gx^2

Question 3

Average Rate of Change:

Answer 3

Finding the slope of the secant line

Question 4

Instantaneous Rate of Change:

Answer 4

Finding the slope of the tangent line

Question 5

Speed

Answer 5

The absolute velocity

Question 6

Finding the Maximum Height in a Problem:

Answer 6

Find the height where velocity is equal to zero.

Question 7

Higher Derivatives:

Answer 7

Position = fx
Velocity = f’x
Acceleration = f’‘x

Question 8

Derivative of Sinx

Answer 8

cosx

Question 9

Derivative of Cosx

Answer 9

-sinx

Question 10

Derivative of Tanx

Answer 10

sec^2x

Question 11

Derivative of Secx

Answer 11

secxtanx

Question 12

Derivative of Cotx

Answer 12

-csc^2(x)

Question 13

Derivative of Cscx

Answer 13

-cscxcotx

Question 14

Chain Rule:

Answer 14

f(g(x))’ = f’(g(x))(g’(x))

Question 15

Implicit Differentiation Solving Steps:

Answer 15

1. Differentiate both sides of the equation with respect to x.
2. Solve for y’.
3. Plug in the point that you need the tangent line of.

Question 16

Derivative of Lnx:

Answer 16

1/x

Question 17

Derivative of Ln(f(x)):

Answer 17

f’x/fx

Question 18

Derivative of B^x

Answer 18

(lnb)b^x

Question 19

Derivative of Logb(x):

Answer 19

1/(x*ln(b))

Question 20

Logarithmic Differentiation:

Answer 20

This is helpful when an equation has a product or quotient with several factors.
You take the ln of both sides fo the equation.

Question 21

Steps to Solving Related Rates:

Answer 21

1. Identify variables and the rates they have related.
2. Find an equation relating the variables and differentiate it.
3. Use given information to solve the problem.

Question 22

Linear Approximation:

Answer 22

Uses the tangent line to the graph of a function at x=a to approximate f(x) for x near a.

Question 23

Linearalization Formula:

Answer 23

L(x) = f’(a)(x-a)+f(a)

Question 24

Critical Point:

Answer 24

Occurs where f’(c) = 0 or DNE.

Question 25

Mean Value Theorem:

Answer 25

f’(c) = [f(b)-f(a)]/[b-a]

Question 26

If f’x>0, then f is:

Answer 26

Increasing.

Question 27

If f’x<0, then f is:

Answer 27

Decreasing.

Question 28

If f’x changes from + to -, then fx is a:

Answer 28

Local max.

Question 29

If f’x changes from - to +, then fx is a:

Answer 29

Local min.