פונקציה מעריכית מורכבת – חלק ב – בעיית אתגר – Stepped Tasks

פונקציה מעריכית מורכבת $e^{f{(x)}}$ - חלק ב'

בעיית אתגר

סעיף א

נתונה משפחת הפונקציות: $g_n{(x)}=e^{f^n{(x)}}$ , $n$ טבעי.

מצאו ביטוי של פונקציה $f(x)$ כך שלכל פונקציה במשפחה זו לא תהיינה נקודות קיצון.
נמקו תשובתכם.

בדקו תשובתכם בעזרת היישומון המצורף.

סעיף ב

1. מצאו ביטוי/ביטויים לפונקציה $f(x)$ כך שהגרפים של $e^{f^3{(x)}}$ , $e^{f^2{(x)}}$ , $e^{f{(x)}}$ יתאימו לגרפים שבסרטוט הבא.
נמקו תשובתכם.

2. מצאו ביטוי/ביטויים לפונקציה $h(x)$ כך שהגרפים של $e^{h^3{(x)}}$ , $e^{h^2{(x)}}$ , $e^{h{(x)}}$ יתאימו לגרפים שבסרטוט הבא.
נמקו תשובתכם.

בדקו תשובתכם בעזרת היישומון המצורף.

יישומון לכתיבה חופשית

ניתן לכתוב ביטוי לפונקציה כלשהי ויופיע הגרף המתאים

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