Lecture 19

Question 1

what is the L’Hospital rule?

Answer 1

if you use substitution for a limit and it produces 0/0 or infinity/infinity, take the derivative of the function, then use substitution again until you get a number

Question 2

what is the order of dominance of ln, a power function and an exponential function?

Answer 2

ln, power function and exponential function

Question 2

how do you find the critical values of a function?

Answer 2

1. find the derivative
2. set the derivative equal to zero
3. factor and solve for x values

Question 3

what is the rule to find the number of turns of a function using the degree?

Answer 3

n-1, where n is the leading degree of the function

Question 4

how can you determine whether a critical value is a local max or min?

Answer 4

1. find the second derivative of the function
2. plug the value or interest into the second derivative
   - if the second derivative produces a positive value, then the critical value is a min
   -if the second derivative produces a negative value, then the critical value is a max

Question 5

what is the formula for tan?

Answer 5

opposite over adjacent

Question 6

what are the steps to solve related rate triangle problems?

Answer 6

1. draw a picture
2. find an equation which is usually the pythegorena theorum
3. implicitly differentiate the equation
4. plug in what you known
5. isolate for what you are trying to find