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# 3.3___after - Section 3.3 Rates of Change The average rate...

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Unformatted text preview: Section 3.3: Rates of Change The average rate of change of f(X) With respect to X for a function f as X changes from to b is fgb)-f(a) . Q '9 b-a Example 1: Find the average rate of change for y = -4x2 - 6 between 2 and 6. £2M<=<o 32-46-3149: ~ISo 531‘ X21 3: “465—49: ~11 vaa rel-+1 (hm/30.: ’/___ <o-’.L : —iSO‘<‘11) (o ~:L —. \YZ‘E- <1 7% Example 2: Drug Control The graph shows federal spending S(t), measured in billions of dollars, as a function of time t, measured in years, on drug contrmms. The average rate of change of spending with respect to time on some interval is defined as the change in spending divided by the change in time. Find the average rate of change in the amount of federal drug control spending With respect to time from 1998 to 2002. .4. h. 3-23 The Federal Drug Control Budget. INS—1W3 VVI IE 3 In E 5 3 .El E. If- ; l 3 2 U ' : = ' I '. -. I I ' ' I . #ﬁsl‘ﬁ “v 75ml“ ‘3.cl°.T‘-ds5\$ \$4“ 1.“? weeﬁﬁﬁeﬁeﬁeeeﬁﬁﬁ 1I:"I,'ur F'f 3033' Presidcm's. Rmunsl F'lr' Ell-32: Elwtml Lia-ml F'r' m-lﬂﬂl: Final Elm-19:: HIIElIJMI'J-LJ' .-"L|| ﬂﬂwr‘l‘um: I"II:I:1| Hudyrl .Jnulhurily'ﬁﬂunl Ellnllgallnlm comemI-znsrwrm Elam-mm. h:. Slide 1-5 a an t — «we» - ram) \ qua "7 “:5 10¢). ~ l‘ﬁK " ll ~7.£ .gg b'llliohAY t a £56 Mlll'mlq A“, Them/stgltaneousrate of change for a function f When X = a is lim fga+h) - ﬂag , h:>0 h provided this limit exists. Example 3: Find the instantane te of change for s(t) = -4t2 - 6 at t = 2. —F(2)‘—-'4-(1)"-‘o —11 «2+» =~¥a+w ~<Q = -\$(4+4L‘+L.1)~g ~z<°~lch~4p4° 462+ k)-Fﬁ\ (-I‘° ~Ibk‘W1-Q‘C' 1") H \ H : ~21<~I\$l4‘4h1+ﬁ : “1%-;qu L\ Example 4: Flu Epidemic Epidemiologists in College Station, Texas, estimate that @ after the ﬂu begins to spread in town, thofthe population infec ed by the ﬂu is approximated by p(t) = t2 + t or Os t s 5. a) Find the average rate of change of p with respect to t over the interval from 1 to 4 days. «‘0 1601+? =26 PG): COL“ -. L ova r372 (have : (‘0 ‘ 4~3 ? 1a-). 0 3 : (is/oPVAGY b) Find and interpret the instantaneous rate of change of p with respect tot at t = 3. we.) : (531+ 3 = \1 K3 m =L3+ki+ c: a) 1‘ (id-Gk +Lfr3—ek W34 LD‘WZO N (qwmwtyk) \ (n) k ‘—"’T/’_ = A75 +7k+lq1742f k : K6790 M‘o k ( 3 Z 742% MM: 3+L‘“ (‘3) K , h~\$o H? ' {V1246 74" : 7+6 = ...
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3.3___after - Section 3.3 Rates of Change The average rate...

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