Week in Review, Math 151, 4.3-4.6, 4.8, 5.1 Week 10

1.Solve each equation for all possible values of x.

a) c)

2. Find the derivative with respect to x of each function.

a)

3. The weight of a bacteria culture doubles every 30 minutes. If initially the culture weighs 28 grams, how long must it grow before it weighs 100 grams?

4. Polonium 210 has a half life of 140 days. If initially 500 mg are present, how many mg will be present after t days? At how many days will it weigh 25 mg?

5. Find the derivative with respect to x of each function.

b)

6. Find the equation of the tangent line to f(x) at (a, f(a)).

i) ii) iii)

7. Simplify each expression.

a) sin(arccos) b) cos(arcsinx) c) sec(arctanx) d) tan(arcsinx)

8. Find the derivative with respect to x of each function.

a) b) c)

9. Evaluate each limit.

b) c)

d) e) f)

10. On what intervals is the function increasing? decreasing? concave up? concave down? Locate any local extrema and inflection points.

a) b)

11. Graphs of f' will be shown. What can you say about f given the graph of f'?