# MATH 2301-102 Fall 2018 Calculus I Recitation 3 Week 4

See the coversheet for instructions and the point value of each problem.

1. For each part below, sketch the graph of a function that satisfies all the conditions or explain why it is impossible to satisfy all the conditions. Conditions given in terms of $$x$$ (such as $$f(x) > 0$$) apply for all $$x$$, whereas conditions given in terms of $$a$$ (such as $$f'(a) > 0$$) apply for a single value $$x=a$$, which you should label.
1. $$f(x) > 0$$, $$f'(x) > 0$$, and $$f''(x) > 0$$
2. $$f(x) < 0$$, $$f'(x) > 0$$, and $$f''(x) > 0$$
3. $$f(x) > 0$$, $$f'(x) < 0$$, and $$f''(x) > 0$$
4. $$f(x) > 0$$, $$f'(x) > 0$$, and $$f''(x) < 0$$
5. $$f(x) > 0$$, $$f'(x) < 0$$, and $$f''(x) < 0$$
6. $$f(x) < 0$$, $$f'(x) > 0$$, and $$f''(x) < 0$$
7. $$f(x) < 0$$, $$f'(x) < 0$$, and $$f''(x) > 0$$
8. $$f(x) < 0$$, $$f'(x) < 0$$, and $$f''(x) < 0$$
9. $$f'(a) = 0$$, and $$f''(x) > 0$$
10. $$f'(a) = 0$$, and $$f''(x) < 0$$
11. $$f'(a) = 3$$, $$f'(x) > 0$$, and $$f''(x) = 0$$
12. $$\displaystyle \lim_{x\rightarrow a^-}f(x)=-2$$, $$\displaystyle \lim_{x\rightarrow a^+}f(x)=1$$, $$f(a)=3$$
13. $$\displaystyle \lim_{x\rightarrow a}f(x)=4$$, $$f(a)=3$$, $$f'(a)=0$$
14. $$f(a)=1$$, $$f(a+1)=2$$, $$f'(x) > 0$$
15. $$f(a)=1$$, $$f(a-1)=2$$, $$f'(x) > 0$$
2. Find values for $$m$$ and $$b$$ so that $$\displaystyle f(x)= \begin{cases} x^2 & \text{if \(x\le -2$$}\\ mx+b & \text{if $$x> -2$$} \end{cases}\) is differentiable at $$x=-2$$.