1. Calculus Review

2. How do I know where f is increasing? O It is where f prime is positive. O Find the derivative and set equal to zero. Use test points to find where f prime is positive or negative.

3. How do I know where f has inflection points? O It is where f double prime equals zero or is undefined and the sign changes. O The f prime function changes from increasing to decreasing or vise-versa. O It is where f prime has maximums or minimums.

4. How do I know if the particle is moving to the left? O It is where f prime is negative. O Find where f prime equals zero. Then check test points on f prime.

5. How do I know if the particle is speeding up or slowing down? O Find v(t) and a(t): If they have the same sign the particle is speeding up. O If they have different signs the particle is slowing down.

6. What is speed? O It is the absolute value of velocity.

7. What do I do if the problem says find the particular solution y = f(x)? O This is asking you to find the original function that represents f. You are probably doing a separable variable problem.

10. What is the limit definition of a derivative?

11. What are the limit rules? O Is it a hidden derivative? O If it’s approaching infinity and it’s a polynomial over a polynomial then use the horizontal asymptote rules. O Can you factor to simplify and just plug in the numbers.

12. How do I prove a function is continuous? Show the left hand limit and the right hand limit are equal and are equal to f(x).

13. Day One Practice

14. Differentiate: arctan 2x

21. x=4 and x=8

24. Day Two Practice

25. t (minutes)0591220 W(t) degrees F54.058.263.168.170

26. Is the previous estimate an overestimate or an underestimate? O It is an overestimate, because the function is always increasing and the right Riemann sum would be above the curve.

29. y – 2 = 2(x + 1)

30. Day Three Practice

33. k = -1

34. X=0 Where are the minimums? X=-1.5 and x = 6