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Math 1300: Calculus I, Fall 2006
Answer Sheet for Review 3
1. Your graph should look something like this:
2. No, limx?0 fprime(x)gprime(x) does not exist.
3. 11.5 and 11.5
4. Answer: 16.
5. (a)
nsummationdisplay
k=0
parenleftbigg 1
2k
parenrightbigg3
=
nsummationdisplay
k=0
1
8k
(b) lim
n??
8(8n ?1/8)
7(8n) =
8
7 cm
3
6. Solution:
(1) Increasing: (??,?2]?[0,?)
Decreasing: [?2,0]
(2) Relative Maximum: (?2,4e?2)
Relative Minimum: (0,0)
(3) Concave Up: (??,?2??2)?(?2 +?2,+?)
Concave Down: (?2??2,?2 +?2)
Inflection Points: x = ?2±?2
1
2
7. f(x) attains its minimum of 1 at x = 0. By the definition of an absolute minimum,
f(x) ? 1 > 0 for all x. The desired inequality follows directly from this.
8. To prove the first statement in the Hint, suppose that the graph of f has a point
P = (b,f(b)) with b in I such that P lies below or on the tangent line lscript and a < b. Then
f(b)?f(a)
b?a ? (the slope of lscript) = f
prime(a).
Since f is differentiable on the open interval I an...

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