21worksheet5 - SOLUTIONS f“ Math 122, Section 021...

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Unformatted text preview: SOLUTIONS f“ Math 122, Section 021 Worksheet 5 Show all work for full credit. 1. Given the following data about a function f(x), 3. Estimate f ’(25). 70w 3 I954“ :54 54 +812 , 4,8 30’25 5 3‘ Z firm/@4720): @515: 8.2 25’20 b. Use your answer from (a) to write the equation of the tangent line to fix) at x=25. pow ( 25,1028) womagzx—zs) yellaezlofx —)7O wa ’2] 2. Suppose a company’s revenue from car sales, R (in thousands of dollars), is a function of advertising expenditure, (1 (in thousands of dollars), so R=f(a). a. What does the company hope is true about the sign off’ ? Why? m con/WM LID/986 10) '5 220591“; We Comma») wade" EX/fCIL their revenue to Mame as tie/r adverbs/lg WWI/LVN "WM; b. What does the statement f ’(10)=2 mean in practical terms? Give units. I10 fie Com/am Cone/nth] spam/5) $[0,000 on aoir/C/irsl , 7W7 C’M Ina‘t’ase fax/{nae 7th“ spend an add/hm} aV000 an Advf/hev? 3. Suppose that f(x) is a function with fl18)=1 0 and f (18)? -12. > a. EstimateflZO). / ()0: 420018 [Om/1+ (18, M30) ‘1’ I {bow/0042112 0,2 woo : 'IZK +Zléo :- F 5’00“ Mr)?” V : »/2x+3lco 13/20) x -12(zo) r310 : 5% b. If the actual value isf(20)=80, what does your answer in (a) tell you about the concavity of f(x) close to x=18? Explain. We actwfl Value )6 3mm Hm W 65hka 50 ‘Hne 3.64/9: at) #00 must am slope M : [v.8 ifl M” 4. Given the graph offlX), sketch the graph of f ’(x) on the same set of axes [Al—CHM . (510??) (mafia IAC + X<,3 MM 0 (,5 0) EQC / "ulna-hu- ullnplnml " It'i‘lflltll ‘ r W o I‘M-“IN + l l, I. ll (0,3) W \) lllflflflllmwa Xd MM L _Illlnllllm gm ML w 5. The graph ofy=f(x) is given. Are the following quantities positive, negative, or zero? a. 1%) s“— b. f’(A) ____0____ c. f”(A) _+__ d./(B>_:__ e-f’(B)O— f.f’<B)_Q___ g. 110 ___’r_ h. f’(C) __i____ i. f"’(C) _-— j. ftD) L k. f’(D) ”— 1. ND) __"_ ...
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21worksheet5 - SOLUTIONS f“ Math 122, Section 021...

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