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Unformatted text preview: MATH 1210  MIDTERM II
VERSION B
November 8, 2006 [10p] Question 1. Check if the function
3 HHS—m) 1“: _ 5'
f(:r)= 5—:t . 25—112 1f33>5 is continuous at a," = 5. [10p] Question 2. Find the derivative of the function: fix] = (1055(13 _ 4) + $38713 [10p] Question 3. Find the slope of the tangent line to the graph at the
point (1.1) for the following function given implicitly: (1‘2 + W = 43:23: .72 [10p] Question 4. Let f(;I') = L :— . (8.) Find the critical points of f.
(b) Find the intervals of increase and decrease.
(c) Find the relative extrema. [10p] Question 5. Two runners are on trails that intersect at right angles,
each runner moving away from the intersection. runner A going east at 15
km per hour and runner B going north at 18 km per hour. At what rate
is the distance between them increasing when runner A is 4 km from the
intersection and runner B is 3 km from the intersection ‘? [10p] BONUS QUESTION. Let f = :32 — 43:. Use the intermediate
Value Theorem to show there is a point in the interval [2,4] such that ﬁx] = —3. if. 1210 ' Midkmhl
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 Spring '09
 man
 Differential Equations, Equations, Intermediate Value Theorem, Continuous function, Intersection, Lenln‘wm oﬁ i=5

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