Question Number 80927 by peter frank last updated on 08/Feb/20
Commented by john santu last updated on 08/Feb/20
$${f}\left({x}\right)={ax}^{\mathrm{4}} +{bx}^{\mathrm{3}} +{cx}^{\mathrm{2}} +{dx}+\mathrm{4} \\ $$$${tangent}\:{line}\:{parallel}\:{to}\:{x}−{axis}\: \\ $$$${f}\:'\left({x}\right)=\mathrm{4}{ax}^{\mathrm{3}} +\mathrm{3}{bx}^{\mathrm{2}} +\mathrm{2}{cx}+{d}\:=\:\mathrm{0} \\ $$$${for}\:{x}\:=\:\mathrm{1}\:{and}\:{x}\:=\:−\mathrm{2} \\ $$$$\Rightarrow\mathrm{4}{a}+\mathrm{3}{b}+\mathrm{2}{c}+{d}=\mathrm{0} \\ $$$$\Rightarrow−\mathrm{32}{a}+\mathrm{12}{b}−\mathrm{4}{c}+{d}=\mathrm{0} \\ $$$${inflection}\:{point}\:{at}\:\left(\mathrm{3},\mathrm{0}\right) \\ $$$${f}\:''\left({x}\right)=\mathrm{12}{ax}^{\mathrm{2}} +\mathrm{6}{bx}+\mathrm{2}{c}\:=\:\mathrm{0}\:{for}\:{x}\:=\:\mathrm{3} \\ $$$$\mathrm{108}{a}+\mathrm{18}{b}+\mathrm{2}{c}=\mathrm{0} \\ $$$${parallel}\:{to}\:{y}\:=\:\mathrm{2}{x}+\mathrm{3}\:{at}\:\left(\mathrm{0},−\mathrm{1}\right) \\ $$$$\mathrm{2}=\:{d}\: \\ $$$${i}\:{think}\:{you}\:{can}\:{solve}\:{it}\:{now} \\ $$$$ \\ $$
Commented by peter frank last updated on 08/Feb/20
$${thank}\:{you} \\ $$
Answered by ajfour last updated on 08/Feb/20
$${y}\left(\mathrm{0}\right)=−\mathrm{1}\:{or}\:\mathrm{4}\:\:? \\ $$
Commented by peter frank last updated on 08/Feb/20
$${i}\:{dont}\:{know}\:{sir}\:{help} \\ $$$${me} \\ $$
Commented by peter frank last updated on 08/Feb/20
$${and}\:{Qn}\:\mathrm{80930} \\ $$
Commented by Kunal12588 last updated on 08/Feb/20
$${if}\:{the}\:{curve}\:{satisfyies}\:{both}\:\left(\mathrm{0},\mathrm{4}\right)\:{and}\:\left(\mathrm{0},−\mathrm{1}\right) \\ $$$${then}\:{the}\:{eq}^{{n}} \:{must}\:{be}\:{implicit}.\:{then}\:{I}\:{don}'{t} \\ $$$${think}\:{we}\:{can}\:{take}\:{the}\:{eq}^{{n}} \:{as}\:{sir}\:{john}\:{took}. \\ $$
Commented by ajfour last updated on 08/Feb/20
$$\left(\mathrm{0},\mathrm{4}\right)\:{and}\:\left(\mathrm{0},−\mathrm{1}\right) \\ $$$${thanks}\:{for}\:{understanding}\:{my} \\ $$$${confusion}\:{Kunal},\:\left({where}\:{r}\:{u}\:{from},\right. \\ $$$$\left.{i}\:{mean}\:{native}\:{place}?\right) \\ $$
Commented by Kunal12588 last updated on 08/Feb/20
$${I}\:{am}\:{from}\:{Bhilai},{Chhattisgarh},\:{India}, \\ $$$${Asia},\:{Earth},\:{Milkyway}\left({I}\:{don}'{t}\:{after}\:{this}\right),\:{well}\:{I}\:{believe}\:{in}\:{multiverse} \\ $$$$\left.{haha}\:{lol}\::\right) \\ $$
Commented by ajfour last updated on 08/Feb/20
$${pleasure}\:{to}\:{know},\:{i}\:{asked}\:{coz} \\ $$$${there}\:{was}\:{an}\:{other}\:{member}\:{by} \\ $$$${the}\:{name}\:{Kunal}..\:{whom}\:{i}\:{knew}, \\ $$$${and}\:{belonged}\:{to}\:{my}\:{town},\:{so} \\ $$$${just}\:{to}\:{confirm}.. \\ $$