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1994BC4 - H?‘-—EC.LIL 4 Let f(x = 6 xl For 0< w< J5...

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Unformatted text preview: H?‘+-—EC.LIL 4. Let f(x) = 6 - xl. For 0 < w < J5, Eet A(w) be the area of the triangle formed by the coordinate axes and the line tangent to the graph of f at the point (w, 6 — wz). (See figure above) (a) Find AU). (13) For what vaiue of w is A(w) amjnimum? ewe“: 10m: tip—x“, o 4 w- 4J1: AC») 2 Area. AOMP 139M Ms) when (w) (9-H): (1,5) eat. W: tj" ({c—wxz) = :m (ac-w} where M = 43%;): - 2w- lé—(Q‘WL)=‘2W (ac—W) é+wl %Evciwercqa‘t = (9+wl; )1 fwiercep‘t = Rw- A(0=;‘:x7x§: = 49 If. (ewe) _ i. (bi’bo'L); b) A(LC}=§Z((9+LJ‘1) a” -+ W, thcm _ _._ [(ur-R((o+w‘)(2w)—~(b+w‘)fl dw- " ‘f “may—7*“ i [(b+wz)(4wL- ((94'u1'1))] ‘fur" ‘ (t+w‘)(3t.r‘.— to) w It _- =0 when Lr=JE 1994 BC4 AOAJ‘) is an mbSqu+€ Min-chagmn when W=JE (0. 5) N5. 0) Nate: Figure not drawn to scale. ...
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