Lecture 10

Question 1

what does it mean if the derivative of a function is not continuous at a point in terms of the derivative?

Answer 1

the derivative does not exist

Question 2

how do you determine if a piecewise function derivative exists at a certain point?

Answer 2

1. find the limit from the left and right side of the function and see if the answers are equal
2. find the derivative of the left and right side functions plug in the point of interest and verify that both answers match

Question 3

when does a derivative not exist at a certain point?

Answer 3

it there is a corner, vertical tangent, or increasing oscillation at that certain point

Question 4

what is the slope of the secant?

Answer 4

the change in y over the change in x between two different points

Question 5

how do you tell if an x value exists in a function?

Answer 5

1. plug the value of interest into the original function and see if a real number comes out
2. find the derivative of the function
3. plug the value of interest into the derivative

Question 6

what does it mean if you see a function with something like (1/x)?

Answer 6

there is increasing oscillation at the point x=0