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Mathematics Senior High

207.3 Q.極値を持たないためにはどうすればいいか? →単調増加または単調減少のグラフなら極値を持たない →つまりf'(x)の符号が変わらない →つまり実数解を1つだけ持つか1つも持たないとき →つまりD=0またはD<0 →D≦0 と記述の方針は理解できていると思うので... Read More

たない。 に変わる。 の値をもとの = (変数4個で笑 であるから, る)。 う, 十分条件でお 確認。 の符号の変化を、現 示している。 基本例題207 3次関数が極値をもつ条件, もたない条件 ①①①① (1) 関数f(x)=x2+ax2が極値をもつとき,定数aの満たすべき条件を求めよ。 (2) 関数f(x)=x6x2+6axが極大値と極小値をもつような定数aの値の範囲 を求めよ。 (3) 関数f(x)=x+ax²+x+1が極値をもたないための必要十分条件を求めよ。 ただし, aは定数とする。 AGUS 指針3次関数f(x) が 極値をもつ ⇔f'(x) の符号が変わる点がある ⇔f'(x)=0 が 異なる2つの実数解をもつ ⇔f'(x)=0 の判別式 D> 0 から、上の例で の関係により 解答 (1) f'(x)=3x2+2ax f(x) が極値をもつための条件は、 f'(x)=0が異なる2つの実 数解をもつことである。 3x2+2ax=0 の判別式をDとする -=a²-3.0=a² と D>0 ここで ゆえに, d²>0 から a = 0 D 154 (2) f'(x)=3x²-12x+6a=3(x2-4x+2a) ロ)+(8+ f(x) が極大値と極小値をもつための条件は,f'(x)=0が異 なる2つの実数解をもつことである。 Altells よって, x2-4x+2a=0の判別式をDとすると 1=(-2)^-1・2a=4-2a から, 4-2a>0より (3) f'(x)=3x2+2ax+1 f(x) が極値をもたないための必要十分条件は,f'(x) の符号 が変わらないことである。ゆえに,f'(x) = 0 すなわち 3x2+2ax+1=0 実数解をもたない。 よって、①の判別式をDとすると ここで ゆえに (a+√3)(a-√3)≦0 ...... 4 D≤0 D=q²-3・1=(a+√3)(a-√3) JERS 極大 y=f(x) x=α ① は実数解を1つだけもつかまたは 4/4-a)=4 £57 ...... 基本 201206 重要 210 778 の係数)>0のとき IV x=B a 極小 3次関数が極値をもつとき, 極大値と極小値を1つずつ もつ。 x(3x+2a)=0 から x=0, a≠0 よって としてもよい。 (3) 2 3 (D>0 ) · |- · - (- / -) - a<2 D=0 (*)CO DO a y=f'(x)) y=f'(x) / y=f'(x) GREY & | (*) D<0は誤り。 x 32 E 3 木 1

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English Senior High

大学受験の長文問題です。 解答がないので答えをお願いします🙏

問題 3 以下の英文を読んで、次の問いに答えなさい。 (*のついた語には語注が ある。) If you are able to step outside and hear many types of birds, you might also have a greater feeling of well-being. Two studies show that hearing diverse birdsongs may help increase our happiness. (A) One study was done by researchers at California Polytechnic State University. A research team studied the effects of birdsong ( 1 ) people walking through a park in the U.S. state of Colorado. A biology graduate student, Danielle Ferraro, led the study. "There could be an evolutionary reason why we like birdsong so much. And the idea is that when we hear birdsong it could signal safety to us," Ferraro says. There could be many other reasons, too. Ferraro states that in some areas around the world birdsong can also signal the arrival of spring and nice weather. Bird diversity, she adds, can also mean a healthy environment. She explained her study to Voice of America (VOA). Ferraro and her team played recorded songs from a diverse group of birds native to the area. They did this on hiking trails in a park in Boulder, Colorado. (2) several weeks, the researchers played recorded birdsong at certain times of the day and other times they did not. Then they talked with hikers after they ( 3 ). Hikers who heard the recorded diverse birdsongs reported a greater sense of well-being than the people who heard simply the natural birds. The researchers suggest that both the bird sounds and biodiversity* can increase feelings of well-being. Ferraro explained that she used native birdsong for the study. This way it would sound as natural as possible. They also did the study during the summer. She explains why this is important. "So the study ( 4 ) in the summer and that's kind of important because the spring is most birds' breeding* season. And if we play the birdsong during breeding season, that might have disturbed them. (B) We didn't want to disturb the birds too much." The study was published in an academic journal called the Royal Society B in December 2020. - 10- ◇M2 (310-15)

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English Senior High

今すぐだと嬉しいです!このワークの答えを無くしてしまい困っているので誰か答えを教えてください🙏

bo school P.198 5.198 198 199 1.00 199 99 00 1 Put the words in the correct order to complete the sentences. 1) I don't like [ being / what /do /to / told ].MICA 2) She would not admit [ him / had / having / a date / with ]. 3) I'm ashamed [ done / thing / a / having / such / silly / of ]. 4) He is angry [in public / laughed / at / been / having / at ]. on the wilds 2 Complete each sentence so that they mean almost the same thing. 1) a) Are you sure that you saw a UFO? b) Are you sure of ( ) ( ) a UFO? 2) a) I'm sorry that I hurt her feelings yesterday. I'm sorry for ( ) ( b) ) her feelings yesterday. 3) a) The boy denies that he didn't tell the truth to his friends. quid d b) The boy denies ( ) ( ) () the truth to his friends. 4) a) The coach was aware that we weren't confident. b) The coach was aware of ( )(_)( ) confident. blool 1006 4 Fill in the blanks so that they mean almost the same thing. 1) a) I can't wait to visit my friend in Okinawa. b) I am looking ( ) ( ) ( 2) a) It is useless to worry about the entrance examination. b) It is ( ) ( ) ( ) about the entrance examination. 3) a) Jill always says she wants to go out on a sunny day.dd?? b) Jill always says she feels ( ) ( 4) a) No one knows what will happen tomorrow. b) There is ( ) ( ) my friend in Okinawa. 3 Fill in the blanks to complete the sentences. B 1) I ( ) ( thinking I've made the same mistake. (同じ間違いをした気がしてならない) )()() in line. (並んで待つことに慣れていない 2) Children aren't ( 3) This book is ( ) ( ) again. (もう一度読む価値がある) salond tog JstosnyM (d) 4) ( )( ) having dinner with us? (私たちと夕食をいかがですか) ) out on a sunny day. JOVE A A ) what will happen tomorrow. Us A The 34 ) ¢X (d) MED I (A) you swiss I (d) ried you had IQ Put it into English - Context writing - 1) 私の祖父母は私の幼い弟と私に会うことを楽しみにしている。 160 2)祖父は子どもたちと遊ぶことに慣れている。 3) しかし彼は幼い弟にいつかめがねを壊されるのではないかと心配している。 (be afraid of) 4) 幼い弟は彼のめがねをつかみとらずにはいられない。 (grab) 5) めがねをかけないことは、祖父にとって危険です。 B

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