بحث دالة بولينوم – سؤال 4

1987
6146

بحث دالة كثيرة الحدود (بولينوم)
ابحث الدالة التالية في المجال:
]𝟒 ,𝟒-[ , اي في المجال 𝟒 ≤ 𝒙 ≤ 𝟒-
𝒚 = 𝒙
𝟐 + 𝟒𝒙 – 𝟓
.1مجال التعريف:
الدالة معرفة في المجال 𝟒 ≤ 𝒙 ≤ 𝟒- .
.2نقاط التقاطع مع المحاور:
تقاطع الدالة مع محور 𝑥 نعوض : 𝑦 = 0
0 = 𝑥2 + 4𝑥 – 5 = (𝑥 – 1) ∙ (𝑥 + 5) = 0 → 𝑥 = 1 , 𝑥 = -5
𝑥 = -5
خارج مجال التعريف لذلك نقطة التقاطع مع محور 𝑥 هي ).(1,0
تقاطع الدالة مع محور 𝑦 نعوض ( 𝑥 = 0مسموح لان 𝑥 = 0داخل مجال التعريف) :
𝑦 = 02 + 4 ∙ 0 – 5 = -5 → 𝑦 = -5
لذلك نقاط التقاطع مع محور 𝑦 هي: ).(0, -5
.3نقاط قصوى وتحديد نوعها (:)Max/Min
نشتق الدالة: 𝑦= 2𝑥 + 4
نساوي المشتقة لصفر ثم نحل المعادلة التي تنتج:
𝑦= 0 → 2𝑥 + 4 = 0 → 𝑥 = -2
نعوض 𝑥 = -2في الدالة لكي نجد الاحداثي 𝑦:
𝑦 = (-2)2 + 4 ∙ (-2) – 5 = -9 → (-2, -9) نقطة شك
نبني الجدول لكي نحدد نوع النقاط القصوى (وايضا لايجاد مجالات التصاعد والتنازل):

نقطة طرف
𝑥 = 4
نقطة اختبار
𝑥 = 0
نقطة شك
𝑥 = -2
نقطة اختبار
𝑥 = -3
نقطة طرف
𝑥 = -4
نعوض نقاط الاختبار
في المشتقة
+ اشارة المشتقة
𝑓(𝑋)
تصرف الدالة )𝑋(𝑓
استنتاج عن الدالة
𝑓(𝑋)
Max (-4, -5) Min (-2, -9) Max (4,27)


يمكن ايضا ان نفحص نوع النقطة القصوى الداخلية عن طريق المشتقة الثانية:
𝑦′′(-2) = 2 > 0 → Min (-2, -9)
نقاط قصوى مطلقة: يمكن ان نستنتج ان للدالة يوجد نقطة صغرى مطلقة وحيدة وهي,
) Min (1, -4لان الاحداثي 𝑦 فيها هو الاصغر على الاطلاق في كل مجال تعريف
الدالة. وايضا يمكن ان نستنتج ان للدالة يوجد نقطة عظمى مطلقة وحيدة وهي,
) Max (4,27لان الاحداثي 𝑦 فيها هو الاكبر على الاطلاق في كل مجال تعريف
الدالة.
.4مجالات تصاعد ومجالات تنازل الدالة:
نستنتج المجالات من الجدول اعلاه:
مجال التصاعد: .
-2 < 𝑥 < 4مجال التنازل . -4 < 𝑥 < -2
.5مجالات موجبة ومجالات سالبة:
نعوض في الدالة 𝑦 = 0لكي نجد النقاط الصفرية للدالة: لقد وجدنا النقاط الصفرية
في بند
2ووجدنا انها: , 𝑥 = 1نضع هذة النقطة ونقاط الطرف على محور 𝑥 ثم
نختار نقاط اختبار مناسبة, نعوضها في الدالة ونحدد اشارة الدالة:
لذلك نستنتج ان: المجال الموجب هو: .
1 < 𝑥 < 4
المجال السالب هو: . -4 < 𝑥 < 1

-4 1

X
0 2
اشارة الدالة (موجب/سالب)
نقاط اختبار (نعوضها في الدالة)
4
.6رسم بياني تقريبي:
حسب البنود السابقة الرسم البياني التقريبي للدالة هو: نقاط الطرف التابعة للمجال تحدد
بدائرة ممتلئة والغير تابعة للمجال تحدد بدائرة فارغة.
X
Y
Min
Max
Max


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  30. I smirked as I unbuttoned the rest of my shirt. I threw it to the washing pile. My breasts fell out as I unhooked my bra. It followed my shirt to the pile. I stroked his hair and closed my eyes. His palm grabbed and squeezed my full youthful breasts. I stood him up and demanded he get naked as soon as possible… that I’d time him. I smirked enjoying the game. Before I could blink he was naked. He looked great. I was still in my school stockings and tartan skirt, my cock and his meeting like a draw bridge between us. He grabs my tits again as though he’d never seen a pair before. Maybe he…
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  31. You looked up from the checklist and gave me the most adorable smile that said, “I hate you” and “I love you” at the same time. I walked around the cart and wrapped my arms around you. “We’re just about done” you said as you looked up at me and smiled. “THANK GOD, finally” I said as i pulled you close and faked a dramatic death on your shoulder. You broke my grip and hit me in the shoulder with the little black notepad, “stop whining, you big baby”, “Marines don’t whine, you just take FOR-EV-ER” I made sure I over annunciated every syllable. You rolled your eyes and walked past toward the…
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  32. I know from talking with her that she is divorced. Her husband left her a few years ago for a younger 20 something model. She has always flirted with me and I have flirted back. It was about quarter to five when my phone rang. It was Kristen, she told me she is about an hour and half away and that she would stop by and bring me the information. Six o’clock came in no time and I got up to freshen up. Everybody had left the office. It made me mad that I was working so many damn hours and everyone else leaves at five. As I walked out of the men’s room, I looked out the door and saw…
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  33. I really don’t get involved in my husband’s business but have met many of his clients and occasionally run some errands for him. Patrick, his client, lived in a very exclusive neighborhood in a wonderful house on a large estate. He was obviously successful but I don’t know what he did or what the papers were that I was delivering to him. It was a hot day so I dressed lightly in a white sundress with the idea of going shopping at the mall after I delivered the papers. Patrick met me at the door wearing a robe. He was a big burly man in his sixties, a bit of a pot belly but ruggedly handsome…
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  34. I knew he’d do almost anything to please them as he was struggling to make money. Little did I know what he had in mind while I was in the bathroom? The following is an account from one of the photographers in the group No sooner had the bathroom door closed behind you, your wife looked across at the owner of the studio in a nervous manner. Now she was on her own dressed in just her tiny undies with her gorgeous body on display. She could not fix her eyes through being so nervous but the owner was not going to miss this opportunity to save his credibility. He quickly suggested to her…
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  35. “Never seen you here before.””Do you come to this hotel so often?” I asked.”It’s a good place to observe people.””And find desperate women.””Just another appealing aspect.””Are you here with Wilson?” I pointed to the sign. “Nah, there’s always some stupid party or reunion here. So, are you a desperate woman?” He placed a hand on my thigh.  The corners of his mouth were turned up and he kept looking me over.  I’m okay with arrogant, but this guy was really sure of himself. His ego was starting to make me nauseous. I realized that I could use him for pleasure, but I imagined the smug…
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  36. Then it came to me; I remembered how excited I became reading about Vivian and Jessica. I felt like I was now Vivian.Pete spread her lips apart and began stroking into her hairy slit. His fingers paid special attention to her swollen hooded little bead. She moaned more, and louder. I undid my blanket and reached into my robe and between my legs. I probably should have put my pjs back on after showering, but I figured they would be off quick enough for my massage, so why bother. Another benefit to not wearing pjs; it’s less inhibiting for my hand to snake its way between my legs. After…
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  37. They caught on her boots and it took him some time to work the leg openings over the large boot tops. She stood there patiently, enjoying his struggle. She knew he could feel the wetness of the panties, smelling her musk. He was getting impatient to bury his face in her softness but she stood there, not helping, just waiting while he struggled with the panties. Finally he got them to her ankles and she leaned over, resting her hand on his shoulder as she lifted each foot, one by one, pulling them free of the panties while he held them firmly in his teeth. He was inordinately pleased by his…
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  38. “Okay Mom! Have a good Trip! I’ll see you on Sunday and I’ll have no More than Maybe ten parties!” i Laughed at my own joke. ” You better not be inviting any girls over either Now Bye” She closed the door and I watched her leave the front yard my 9 inch cock aching to be stroked, after i saw the car drive away i went on my laptop and well did whatever a sixteen year old boy would do when he was horny, Yes i stroked my 9 Inch cock until i exploded all over. After a good Session of Masturbating i headed downstairs for something to eat, man was i hungry “Damn, Nothing to eat Maybe i’ll go to the…
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  39. The Vice-Principal savoured the sight of her nemesis in this sexually vulnerable and available pose, and took more pictures from several angles of her boss, who was now naked apart from her shoes, the skirt up around her waist and the large bra from which her huge tits had been extracted. Then Jacquelyn put the camera away in her bag and withdrew her favourite and largest strap-on – one which she had not had any opportunity to use on another woman for many months. She stripped off her flimsy thong and buckled the dildo in its place, over the straps of her suspender belt. The bitch’s cunt is so…
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  40. 1.)I have always had a vivid imagination. 2.)Im a nympho with a porn addiction (thank goodness for xnxx!)3.) The more I experience the more extreme and even gross my porn selection and fantasies become. I gave up my crazy lifestyle about a year ago when I met my husband. I went from orgies to him literally overnight. He kept me so consumed working on his problems and proving to him that I wanted only him that I even fooled myself into believing I was “cured”.I have been faithful to him throughout our relationship, although there has been plenty of temptation. Now he’s starting to…
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