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Mathematics Senior High

青い丸のとこについて質問です。M(a)−m(a)がaの関数とかかれていますが、M(a)やm(a)自体もaの関数ですよね?初歩的な質問で申し訳ないです。回答お願いします。

Date 7 2次関数の最大・最小/定義域が一定区間 - αを定数とする. 2次関数y=x-2ax+3の0≦x≦2 における最大値 M (α) を,最小値をm(4) とする.M(a), m(a)を求めよ. またM(a) -m (α) の最小値を求めよ. (類摂南大) y=d(x-p)+qのグラフ YA d<0 平方完成 2次関数の値の変化の様子をとらえるには, y=d(x-p2+qの形 (平方完成) にすることが絶対的であって (が1か所にしか登場しないので, 関数値の変化の様子がよく 分かるようになる) 関数値は YA d>0 d0....... |-plが大きいほど大きくなる d<0......x-pが大きいほど小さくなる というように変化することが分かる. q O p x 2 100 最大 最小 下に凸(2次の係数が正)の場合、区間α≦x≦ßにおける最大・最小は下のよう。 al m(a け 最大はこれらを使って y=f(x) (軸) ① (軸) ② ④ ⑤ 6 最大 : 最大 最大: 最小 最小 最大: (7) 最小 X x 84 a B α ẞx a β x 最小はこれらを使って a β a B a Bx aβ a+β 区間の中点 2 最小値は,対称軸が区間内であれば頂点のy座標 (上図②), なければ対称軸に近い方の端点のy座標 である (1,③) 最大値は, 対称軸から遠い方の端点のy座標, つまり対称軸が区間の中点より左側に あればf (B) (④ ⑤), 右側にあればf (α) (⑥ ⑦) である. 解答量 f(x)=x-2ax+3 ⑦ とおくと,f(x)=(x-a)-α+3であるから, y=f(x)のグラフは下に凸で,軸はx=αである. 区間 0≦x≦2における最大値は, 区間の中点がx=1であることから, a≦1 のとき,M(α)=f(2)=-4a+7 (アに代入した) 1≦αのとき,M(a)=f(0)=3 また,0≦x≦2における最小値は,軸が区間に入るかどうかに着目して, 0≦a≦2のとき,m(a)=f(a)=-α+3 a<0 のとき,m(a)=f(0)=3 2<a のとき, m(α)=f(2)=-4a+7 以上からM(a), m(a), M(a)-m(α) は次のようになる。 直線 b=-4a+4 64 [注] M(a), m (α) はαで表され ることから,M(α) -m (a) は a の関数と見ることができる. 軸と区間の中点の位置関係で場 合分けする (上図 ④と⑤のケース と, ⑥と⑦のケースとで場合分 け). 上図の② ①③で場合分けする. mayの場合分 直線 b=4a-4 [0≤a≤2 けは,a≦0 12≦a a M(a) m(a) M(a)-m(a) a<0 -4a+7 0≤a≤1 -4a+7 3 -a²+3 -4a+4 (a-2)² 1≦a≦2 3 - a²+3 2<a 3 -4a+7 a² 4a-4 b=a2 b=(a-2)2 b=M(a)-m(a)のグラフは右図のようになるから, a=1のとき最 としてもよい 境界のα=0, 2 では2つの m(α) の式で通 用し,同じにな るかでミスを 2 a チェックでき

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TOEIC・English Undergraduate

青くしてある文の文構造と訳し方を教えていただきたいです🙇‍♀️ また、mainstream America の語順に違和感を感じていて、(American mainstream とした方が正しくない?と思ってしまいます、、)それも解説いただきたいです。

Neil Hello. This is 6 Minute English from BBC Learning English. I'm Neil. Georgie And I'm Georgie. Neil If I told you I'd been for a walk to see Big Ben and Buckingham Palace, you'd know straight away I was in London. Georgie But what if my walk went past cafes selling mozzarella and ricotta where I smelled freshly made cannolis and focaccia... Where would I be then? Neil Focaccia and mozzarella... you'd be in Italy, right? Georgie Yes, Italy, or 'Little Italy' to be exact - the neighbourhood in some cities where Italian communities settled and made their home. Neil These Italian arrivals opened shops and cafes selling food to their own communities. Soon dishes like spaghetti and meatballs attracted the attention of local people, and gradually Italian food became famous around the world. In this programme, we'll be taking a walk through two Little Italys, one in Argentina, the other in New York, and, as usual, we'll be learning some useful new vocabulary as well. But before that, I have a question for you, Georgie. According to a recent YouGov poll, which Italian food is most popular with British diners? Is it: a) pizza? b) lasagne? or c) garlic bread? Georgie I think it must be pizza. Neil Okay, Georgie, I'll reveal the answer at the end of the programme. One country Italians moved to was Argentina. In 1898, Giuseppe Banchero arrived in the neighbourhood of La Boca, the Little Italy of Buenos Aires, where many Italian immigrants started restaurants. Here, Hugo Banchero, grandson of Giuseppe, tells his story to Veronica Smink, reporter for BBC World Service programme, The Food Chain: Hugo Banchero Well, my grandfather came from Italy, from Genoa, from Liguria. He was born in the centre of Genoa and arrived here in 1898 at the age of seven and a half, and this pizzeria where we are was founded on March 28, 1972. We have been here for 91 years. Veronica Smink So what culinary traditions did they bring with them? Hugo Banchero Well, our culinary tradition is pizza, and we incorporated the faina from Genoa, which is a pizza with chickpea flour... Georgie In 1898, Giuseppe founded his pizzeria - a restaurant selling pizza. When a business is founded, it's established someone starts it, or sets it up. Neil Giuseppe brought the culinary traditions from his home in Liguria in northern Italy, including regional pizzas like faina and fugazzetta. The adjective culinary describes anything connected with cooking. Georgie But probably the best-known Little Italy in the world is an area of Manhattan's Lower East side in New York. Ninety percent of Italian immigrants who arrived in the US at the turn of the century came through this neighbourhood. Neil De Palos, one of the original shops selling Italian food in Little Italy, has been serving customers for 113 years. Here, Lou De Palo, co-owner and great-grandson of the original owner, Salvino, explains more about his family history to BBC World Service programme, The Food Chain: Lou De Palo 1925... when my grandmother, Concetta, and my grandfather, Luigi, got married, they open their own shop... it's the shop we continue today being the fourth generation working alongside my sister, Maria, my brother, Sal, and our children, the fifth generation. Our business has expanded; expanded to present the full food culture of the 20 regions of Italy. Little Italy is the stepping stone of the Italian immigrant. This is where many of the Italians first came through Ellis Island, and then settled here, and then eventually moved into mainstream America throughout the rest of the country. Georgie Lou De Palo is the fourth generation of his family to run the shop, and his children will be the fifth. Phrases like fourth or fifth generation describe the children of people whose parents immigrated to a particular country.

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