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<_ebqbgb klZe• lZ af•gg• Nmgdp•y

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AZ^Zggy nmgdp•€ Nmgdp•y \\Z`Z}lvky aZ^Zghx ydsh

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QZkldh\bf agZq_ggyf nmgdp•€ gZab\Z}lvky l_ €€ agZq_ggy yd_ \•^ih-

x = x0 >ey ihagZq_ggy qZkldh\h]h agZ- q_ggy nmgdp•€ ijb x = x0 \`b\Z}lvky kbf\he f (x0) Z[h y (x0).

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H[eZklv af•gb nmgdp•€ Kmdmig•klv mk•o agZq_gv y, sh h^_j`Zg• a]•^gh

nmgdp•hgZevgh€ aZe_`ghkl• ml\hjxxlv fgh`bgm ydZ gZab\Z}lvky h[eZklx af•gb nmgdp•€.

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lbo ijb ydbo agZf_ggbd ^jh[m x2 – 7 x ^hj•\gx} gmex lh[lh hdj•f x lZ x p•

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Ih[m^h\Z ]jZn•d•\ nmgdp•c

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>ey ih[m^h\b ]jZn•dm nmgdp•€ y = f (x aZa\bqZc ^•xlv lZdbf qbghf gZ- ^Zxlv Zj]mf_glm ^_d•evdZ qZkldh\bo agZq_gv • dhjbklmxqbkv ZgZe•lbqgbf \b- jZahf nmgdp•€ h[qbkexxlv \•^ih\•^g• agZq_ggy nmgdp•€

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M1 (x1,y1), M2 (x2,y2), M3 (x3,y3), ..., Mn (xn,yn).

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Ydsh nmgdp•y iZjgZ ^ey ih[m^h\b ]jZn•dm ihlj•[gh:

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2) Ih[m^m\Zlb ©^a_jdZevg_ \•^h[jZ`_ggyª \•^ghkgh hk• Hm ]jZn•dm hljbfZgh- ]h \ i

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qbgb Lhfm ]jZn•d g_iZjgh€ nmgdp•€ jhalZrh\Zgbc kbf_ljbqgh \•^ghkgh ihqZldm dhhj^bgZl.

>ey ih[m^h\b ]jZn•dm g_iZjgh€ nmgdp•€ ihlj•[gh

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2) Ih[m^m\Zlb djb\m kbf_ljbqgm \•^ghkgh ihqZldm dhhj^bgZl djb\•c ydZ ih[m^h\ZgZ \ i

P• \eZklb\hkl• iZjgbo lZ g_iZjgbo nmgdp•c \bdhjbklh\mxlv ijb ih[m^h\• ]jZn•d•\ nmgdp•c

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Jha\¶yahd. <bagZq_ggy iZjghkl• g_iZjghkl• nmgdp•€ fh`_ kijhklblb ih[m^h\m ]jZn•dm lhfm h[qbkebfh f (– x):

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Z g• ^h iZjgbo Z g• ^h g_iZjgbo nmgdp•c P_ nmgdp•y aZ]Zevgh]h \b]ey^m

IjbdeZ^ 3 GZ •gl_j\Ze• ydbc gZe_`blv ^h h[eZkl• •kgm\Zggy nmgdp•€ jha\¶yaZlb aZ^Zqm lZ[mex\Zggy nmgdp•€ y = 2x2 – 1 lZ ih[m^m\Zlb ]jZn•d 1gl_j\Ze lZ djhd lZ[mex\Zggy

\b[jZlb ^h\•evgh

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2. ih[m^h\Z ]jZn•dZ nmgdp•€

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Ih[m^m}fh lZ[ebp• agZq_gv Zj]mf_glm • nmgdp•€ aZ ^hihfh]hx _e_dljhggbo lZ[ebpv

MS Excel (Calc).

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NhjfZlbjh\Zgb_: Ihem`bjguc ^ey Calc @bjguc ), Ih p_gljm =hjb- ahglZevgh ih p_gljm >Ze• m ^•ZiZahg dhf•jhd A2:A ihlj•[gh \\_klb agZq_ggy af•ggh€ x: -1,0; - P• agZq_ggy Zj]mf_glm kl\hjxxlv Zjbnf_lbqgm ijh]j_k•x LZdbf qbghf aZih\gblb ^•ZiZahg A2:A agZq_ggyfb Zj]mf_glm yd• af•gxxlvky a djhdhf

fh`gZ [m^v-ydbf kihkh[hf aZih\g_ggy dhf•jhd qe_gZfb Zjbnf_lbqgh€ ijh]j_k•€

Kihk•[ >ey MS Excel: <\_klb \ dhf•jdm : i_jrbc qe_g Zjbnf_lbqgh€ ijh]j_k•€ (- ihl•f \bdhgZlb gZklmigm ihke•^h\g•klv dhfZg^ IjZ\dZ → AZihegblv → Ijh-

]j_kkby lZ aZih\gblb ^•Zeh]h\_ \•dgh Ijh]j_kkby yd ihdZaZgh gZ jbk

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>ey Calc H[jZlb ^•ZiZahg dhf•jhd yd• fZxlv [mlb aZih\g_gg• $ $ ihl•f \bdhgZlb gZklmigm ihke•^h\g•klv dhfZg^ IjZ\dZ → AZihegblv → Jy^u lZ aZih\gblb

^•Zeh]h\_ \•dgh AZihegblv jy^u yd ihdZaZgh gZ jbk

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Kihk•[ Ihke•^h\g•klv hi_jZp•c h^gZdh\Z ^ey h[ho lZ[ebqgbo ijhp_khj•\ <\_klb \ dhf•jdm : i_jrbc qe_g Zjbnf_lbqgh€ ijh]j_k•€ - \ dhf•jdm : – ^jm]bc qe_g -0,9),

ihl•f \b^•eblb h[b^\• dhf•jdb lZ ijhly]gmlb aZ fZjd_j aZiheg_gby ^h hklZggvh]h qe_gm ijh]j_k•€

Kihk•[ Ihke•^h\g•klv hi_jZp•c h^gZdh\Z ^ey h[ho lZ[ebqgbo ijhp_khj•\ >ey \bdhjbklZggy pvh]h kihkh[m ihlj•[gh ^_sh ^h^Zlb – \\_klb \ dhf•jdm D1 agZq_ggy djhdm

0, >Ze• \\_klb \ dhf•jdm : i_jrbc qe_g Zjbnf_lbqgh€ ijh]j_k•€ - \ dhf•jdm : –

nhjfmem $' ihl•f \b^•eblb dhf•jdm : lZ ijhly]gmlb aZ fZjd_j aZiheg_gby ^h hklZggvh€ dhf•jdb :

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IjZ\dZ → <klZ\blv Z[h aZ ^hihfh]hx fZjd_jZ aZiheg_gby).

>ey hnhjfe_ggy lZ[ebp• g_h[o•^gh \b^•eblb ^•ZiZahg dhf•jhd : < lZ h[jZlb NhjfZl → Yq_cdb >Ze• ^ey \•^h[jZ`_ggy m agZq_ggyo Zj]mf_glm • nmgdp•€ ^\ho agZd•\

i•key dhfb gZ aZdeZ^p• Qbkeh ^ey Calc QbkeZ) h[bjZ}lvky ihlj•[gbc nhjfZl gZ aZdeZ^p• <ujZ\gb\Zgb_ \dZam}lvky \bj•\gx\Zggy l_dklm ih p_gljm gZ aZdeZ^p• =jZgbpZ

H[jZfe_gb_ h[bjZ}lvky lbi <k_ ]jZgbpu.

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\ ]jmi• JZaf_s_gb_ h[jZlb i_j_fbdZq kijZ\Z gZ aZdeZ^p• Ih^ibkb ^Zgguob ke•^ \dZaZlb i_j_fbdZq g_l.

>ey Calc gZkljhx\Zggy ^•ZiZahg•\ ^Zgbo ^ey dh`gh]h jy^m ^Zgbo >ey jy^m ^Zgbo y ke•^ m ihey \\h^m \\_klb \•^ih\•^gh GZa\Zgb_ í Ebkl% AgZq_gby O í

Ebkl : : AgZq_gby Y í Ebkl% %

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Hlh[jZ`Zlv k_ldm Hkv O lZ Hkv Y \klZgh\blb ijZihj_pv IhdZaZlv e_]_g^m lZ i_j_fbdZq kijZ\Z

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>ey dhj_]m\Zggy ^•Z]jZf ihlj•[gh

∙i_j_f•klblb i•^ibk gZa\b \•k• Ox aZ ^hihfh]hx fbr•

∙i_j_f•klblb i•^ibk gZa\b \•k• Oy aZ ^hihfh]hx fbr• lZ af•gblb dml

ih\hjhlm gZa\b \•k• \b^•eblb €€ lZ \ dhgl_dklghfm f_gx MS Excel h[jZlb

NhjfZl gZa\Zgby hkb → <ujZ\gb\Zgb_ → Hjb_glZpby – ]jZ^mk•\ ^ey Calc: K\hckl\Z h[t_dlZ → <ujZ\gb\Zgb_ → GZijZ\e_gb_ l_dklZ);

∙ >ey ]jZn•dm MS Excel fh`gZ s_ ^ey gZhqghkl• \klZgh\blb [•ebc nhg

h[eZkl• ih[m^h\b ]jZn•dm \ dhgl_dklghfm f_gx h[jZlb NhjfZl h[eZklb ihkljh_gby).

<•^dhjb]h\Zg• ]jZn•db nmgdp•c ihdZaZg• gZ Jbk 1.5.

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Kihkh[b aZ^Zggy nmgdp•€

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\•^ghkylvky Z lZ[ebqgbc [ ]jZn•qgbc \ ZgZe•lbqgbc ] keh\_kgbc Z LZ[ebqgbc kihk•[ aZ^Zggy nmgdp•€

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