{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 0 12 0 0 0 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Fo nt 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 0 12 128 0 128 1 2 1 2 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 0 11 0 128 128 1 2 1 2 0 0 0 0 0 0 } 0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "PRUBEH FUNKCE " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Zde se zada funkcni predpis:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f:=x->x^4-x^2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "1) ELEMENTARNI VLASTNOSTI:" }}{PARA 0 "" 0 "" {TEXT -1 15 "Definicni obor:" }}{PARA 0 "" 0 "" {TEXT -1 37 " zatim umi jenom body nespojitosti:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "readlib(discont);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "body_n espojitosti:=discont(f(x),x)[];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Sudost - lichost:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "if evalb(f (-x)=f(x)) then print(`funkce je suda`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "elif evalb(f(-x)=-f(x)) then print(`funkce je licha`)" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "else print(`funkce neni ani suda an i licha`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "2) POLOHA GRAFU: " }}{PARA 0 "" 0 "" {TEXT -1 19 "Pruseciky s osou x:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "pruseciky_s_x:=allvalues([solve(f(x)=0)])[];" }} }{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Prusecik s osou y:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 "f(0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "G raf je nad osou:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(f(x)>0); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Graf je pod osou:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "solve(f(x)<0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "3) MONOTONOST:" }}{PARA 0 "" 0 "" {TEXT -1 15 "Prvni derivace:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "diff(f(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "si mplify(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(\"); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "df:=D(f);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Stacionarni body:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "stacionarni_body:=allvalues([solve(df(x)=0)])[];" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "evalf((stacionarni_body));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Funkcni hodnoty ve stacionarnic h bodech:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f_stac:=map(f,[stacion arni_body]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(f_ stac);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "factor(f_stac);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Funkce je rostouci:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(df(x)>0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Funkce je klesajici:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solv e(df(x)<0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "4) KONVEXNOST, KONKAVNOST:" }}{PARA 0 "" 0 "" {TEXT -1 15 "Druha derivace:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(f(x) ,x,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(\");" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ddf:=D(D(f));" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 16 "Overeni extremu:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "znamenka_ddf:=map(proc(b) if (evalf(ddf(b))>0) then evalf(ddf(b) ), print(b,` je lokalni minimum`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "elif (evalf(ddf(b))<0) then evalf(ddf(b)), print(b, `je lokalni ma ximum`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "else `Nelze rozhodnout` " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "fi end, [stacionarni_body]);" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Inflexni body:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "inflexni_body:=allvalues([solve(ddf(x)=0,x)])[]; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "evalf(inflexni_body);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Funkcni hodnoty v inflexnich bo dech:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f_infl:=map(f,[inflexni_bo dy]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(f_infl); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "factor(f_infl);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Funkce je konvexni:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve(ddf(x)>0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Funkce je konkavni:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve (ddf(x)<0,x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "5) ASYMPTOTY " }}{PARA 0 "" 0 "" {TEXT -1 24 "Asymptot y bez smernice: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "limity_zleva:=m ap(proc(b) limit(f(x),x=b,left) end, [body_nespojitosti]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "limity_zprava:=map(proc(b) limit(f(x),x=b,right) end, [body_nespojitosti]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalf(\"); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Asymptoty se \+ smernici:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "kp:=limit(f(x)/x,x=inf inity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "qp:=limit(f(x)-k p*x,x=infinity);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Asypmtota do \+ plus nekonecna je:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "if (kp=infin ity or qp = infinity or kp=-infinity or qp=-infinity) then print(`Nema asymptotu se smernici do plus nekonecna`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "else y=kp*x+qp" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "f i;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "km:=limit(f(x)/x,x=-i nfinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "qm:=limit(f(x) -km*x,x=-infinity);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Asypmtota \+ do plus nekonecna je:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "if (km=in finity or qm=infinity or km=-infinity or qm=-infinity) then print(`Nem a asymptotu se smernici do minus nekonecna`)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "else y=km*x+qm" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "f i;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "7) GRAF" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "plot(\{f(x)\}, x=- 2..2,y=-1..3,discont=true,thickness=2,scaling=constrained);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 4 0" 14 } {VIEWOPTS 1 1 0 1 1 1803 }