֘Ay[Wɂ̃Ot}𗘗pĂD

\

\Ƃ́C֐$y=f\left(x\right)$  ̃Ot̊T߂ɁC${f}^{\prime }\left(x\right)$  ̕߂Ċ֐$f\left(x\right)$  ̑ь̗lq\ɂ܂Ƃ߂̂łD

 $x$ $\cdots$ $a$ $\cdots$ $b$ $\cdots$ $c$ $\cdots$ ${f}^{\prime }\left(x\right)$ + 0 - 0 + 0 - $f\left(x\right)$ $↗$ $f\left(a\right)$ɑl $↘$ $f\left(b\right)$ɏl $↗$ $f\left(c\right)$ɑl $↘$

L̑\Ot̊TƁC̐}̂悤ɂȂD

\̏

֐$f\left(x\right)={x}^{3}+3{x}^{2}-9x+5$  \̈ʓIȏD

1. ${f}^{\prime }\left(x\right)=0$  𖞂$x$  ̒l߂Di ${f}^{\prime }\left(x\right)=0$  𖞂$x$  ̒lŊ֐$f\left(x\right)$  ɑ傠邢͋ɏɂȂDj

$\begin{array}{ll}{f}^{\prime }\left(x\right)\hfill & =3{x}^{2}+6x-9\hfill \\ \hfill & =3\left({x}^{2}+2x-3\right)\hfill \\ \hfill & =3\left(x+3\right)\left(x-1\right)\hfill \end{array}$

āC ${f}^{\prime }\left(x\right)=0$  𖞂$x$  ̒ĺC$x=-1,3$  łD ߂͈͂ő\쐬Ɖ̂悤ɂȂD
 $x$ $\cdots$ $−3$ $\cdots$ $1$ $\cdots$ ${f}^{\prime }\left(x\right)$ 0 0 $f\left(x\right)$

2. ɁC${f}^{\prime }\left(x\right)$ ̕ƏC$f\left(x\right)$̑ŎDi$f\left(x\right)>0$  ł͊֐$f\left(x\right)$  ͑C$f\left(x\right)<0$  ł͊֐$f\left(x\right)$  ͌Dj

 $x$ $\cdots$ $−3$ $\cdots$ $1$ $\cdots$ ${f}^{\prime }\left(x\right)$ + 0 - 0 + $f\left(x\right)$ $↗$ @@@ $↘$ @@@ $↗$

3. Ōɒl̒l߂D

$f\left(-3\right)$$={\left(-3\right)}^{3}+3·{\left(-3\right)}^{2}-9·\left(-3\right)+5$$=32$

$f\left(1\right)$$={\left(1\right)}^{3}+3·{\left(1\right)}^{2}-9·\left(1\right)+5$$=0$

 $x$ $\cdots$ $−3$ $\cdots$ $1$ $\cdots$ ${f}^{\prime }\left(x\right)$ + 0 - 0 + $f\left(x\right)$ $↗$ 32 $↘$ 0 $↗$

֐$f\left(x\right)={x}^{3}+3{x}^{2}-9x+5$   ̃OtD̑\ƔrĂ݂悤D

z[>>JeS[>>>>\

ŏIXVF 2020N41