MA 131-006 | Page 3

You should be able to:

Determine whether the limit exists by looking at the graph of . Sec 1.4
Draw the graph of a function in which the limit does not exist. Sec 1.4 (also, see Test 2 practice problems)
Determine whether a function $\text{[math]}$ is differentiable at a point $\text{[math]}$ by looking at the graph for $\text{[math]}$ . Sec 1.5
- Recall that is differentiable at a point when the following limit exists: exists.
Determine whether a function $\text{[math]}$ is continuous at a point.
- Recall that is continuous at a point when the limit exists is equal to the value . Sec 1.5
Interpret the derivative of $\text{[math]}$ at a point as the (instantaneous) rate of change of $\text{[math]}$ . Sec 1.8
- In populations applications: we call the derivative the growth rate
- In physical applications: we call the derivative velocity
Compute the average rate of change, and compare it to the derivative at a point. Sec 1.8
Interpret the second derivative of $\text{[math]}$ at a point as the (instantaneous) rate of change of the rate of change of $\text{[math]}$ . Sec 1.8
- In population application: we can the second derivative the rate of change of the growth rate
- In physical applications: we call the second derivative acceleration
Compute the second derivative Sec 1.6-1.7
- I will specifically test you on using the general power rule. Sec 1.6
Given a function compute its intervals of increasing and decreasing Sec 2.2
Given a function compute its relative minima and maxima Sec 2.3
Given a function compute its intervals of concavity Sec 2.2
Given a function compute its inflection points Sec 2.3
Use the above information to sketch the graph of $\text{[math]}$ Sec 2.2-2.4
- You will not be asked to find the and intercepts for .
Given information about , , and , at a point sketch the graph of near the point . Sec 2.2
Interpret intervals of increasing and decreasing, relative maxima and minima, and concavity in applications (focus on physical applications) See Application of derivative HW and examples from lecture
Given information about $\text{[math]}$ and $\text{[math]}$ (in a graphical form) answer questions about $\text{[math]}$ . Sec 2.2
- Specifically try numbers 23, 24, 43, and 44 from Sec 2.2; note that number 44 is the test review problem number 4