Chapter 6: Derivatives And Theorems

Question 1

Mean Value Theorem

Answer 1

For a function where you always have an instantaneous rate of change, the average rate of change will be equal to the instantaneous rate of change somewhere in the region where you’ve take the average.

Question 2

Average rate of change

Answer 2

Total distance/total time

Question 3

Instantaneous rate of change

Answer 3

Average rate of change at any specific time.

Question 4

Rolle’s THeorem

Answer 4

A special case of the mean value theorem. If the average rate of change is zero, then the instantaneous rate of change equals zero somewhere along that path.

Question 5

L’Hopital’s Rule

Answer 5

If you have some functions f(x) or g(x) that approach 0 as x->c

Lim. F(x)/g(x)=Lim f’(x)/g’(x)
x->c X->c

We do this if we get a limit=0/0.

Question 6

L’hopitals Rule Part 2 with infinity

Answer 6

x->c goes to infinity for
Lim f(x)/g(x) =. Lim f’(x)/g’(x)
X->C. X->c

If lim F(x)=infinity
X->c
Lim. g(x)=infinity
X->c

This is used if limit=infinity/infinity

Question 7

L’Hopitals 3-step plan

Answer 7

1. Check limit of top & bottom
2. Differentiate the top & bottom
3. .Calculate limit of derivatives