Math 161 Calculus I

Reading Outlines

You should answer these questions as you read the text.

Section 3.1

1. Explain in your own words what an antiderivative is.
2. Let y = f (x) = x². Explain in your own words what each of these means:
   a.$${\frac{df}{dx}}$$        b.$${\frac{dy}{dx}}$$        c.$${\frac{dy}{dx}}$$$$\mid_{x=3}^{}$$ = 6

3. Review question: what is the domain of a function?
4. What is the domain of the function f'?
5. What is a power function? Give three examples (at least one with a negative or fractional exponent).
6. Carefully explain the computations on page 183.
7. Let f (x) = x² + 1. Use the definition to find f'(x). Review Example 1 to help out.
8. Explain the power, sum, and constant rules for derivatives.
9. Describe the problem of ``antidifferentiation.''
10. Explain how we found the antiderivative Q in Example 5.
11. What role did the constant k play in finding the antiderivative S in Example 5?
12. Why aren't antiderivatives unique? Part of answering this question involves explaining why the derivative of a constant is zero!
13. What is the power rule for antiderivatives?
14. What is the moral of finding antiderivatives?? Remember this!!!