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数学 高校生

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重要 例題 218 4次関数が極大値をもたない条件 00000 関数f(x)=x4-8x3+18kx2 が極大値をもたないとき, 定数kの値の範囲を求め よ。 XAS 4次関数 f(x) x=pで極大値をもつ [福島大] 基本 211,214 x Þ f'(x) + 0 f(x) 極大 \ x=pの前後で3次関数f(x)の符号が正から負に変わる であるから、f'(x)の符号が「正から負に変わらない」条件を 考える。 3次関数f(x) のグラフとx軸の上下関係をイメー ジするとよい。 なお、解答の右横の図はy=x(x2-6x+9k) のグラフである。 f'(x)=4x-24x2+36kx=4x(x2-6x+9k) f(x) が極大値をもたないための条件は, f'(x) = 0 の実数 解の前後でf'(x) の符号が正から負に変わらないことであ ある。このことは, f'(x)のx3の係数は正であるから, 3次 方程式 f(x) = 0 が異なる3つの実数解をもたないことと 同じである。 k≥1 y k>1 k=1 347 3 x 解答 f'(x) = 0 とすると x=0 または x2-6x+9k=0 よって, 求める条件は,x2-6x+9k=0が k=0 y [1] 重解または虚数解をもつ [2] x=0 を解にもつ [1] x2-6x+9k=0 の判別式をDとすると D≤0 1-k≤0 35 12121=(-3)2-9k=9 (1-k) であるから 求め方は よって k≧1 [2] x2-6x+9k=0に x=0を代入すると k=0 したがって k=0, k≧1 おける関数の 6 x I 一般に, 4次関数 f(x) [4次の係数は正] に対し、f'(x)=0 参考 [4次関数の極値とグラフ] 3次方程式で,少なくとも1つの実数解をもつ。 その実数解をαとし、他の2つの解が実数 あればβ, y とする。このとき, y=f(x) のグラフは、次のように分類できる。 特に, 極大値を るのは①の場合だけである。 あり ける 小が入れ替わる)

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英語 高校生

この解答であっているのかそしてなぜほかの答えではだめなのか教えて頂きたいです。

Part 5 Daily Life Incomplete Sentences Select the best answer to complete the sentence. Then choose the letter (A), (B), (C), or (D). 1. All participants have to arrive ten minutes before ------- scheduled appointments. (A) they (B) their (C) them (D) themselves 2. At the book reading workshop, authors read books ------- to children. Text Completion Select the best answer to complete the text. Then choose the letter (A), (B), (C), or (D). Questions 9-12 refer to the following notice. Security Notice by Artist Request The use of cellphones, cameras, smart watches or recording devices will not be permitted during tonight's performance. Guests are encouraged to leave these items in their home or vehicle to entry. Failure to comply with this ------ your 11. 9. policy will result in ---- from the venue without a refund. We greatly. 10. (A) fully (B) aloud 3. We are pleased to (A) welcoming (C) noisy (D) over ------- a new exchange student from Canada. (B) welcome (C) welcomed (D) welcomes 4. Use this robot vacuum cleaner after reading the ------- carefully.A.2 (A) systems 5. The order can -------- (A) ships (B) policies anywhere in the world. (B) to ship (C) applications (C) be shipping (D) be shipped 6. Steven began a bakery more than 20 years ------- (A) last (B) ago (C) past cooperation in creating a phone-free viewing experience. ------ 12. Thank you for your understanding. Central Theater directions A 9. (A) once (B) when (C) advance (D) prior (D) before 10. (A) remove 11. (A) anticipate (B) removing (C) removal (D) removed (B) acknowledge (C) acquire (D) appreciate 12. (A (D) automate Further details about this policy can be found on our website. (B) Come celebrate our 25th anniversary this Saturday from 5:00 P.M. (C) For information on group rates and private events, check online. (D) Check for details to see if you qualify for exclusion to this rule. 7. The air conditioner we bought was designed to turn off -------. (A) automatic (B) automatically (C) automated 8. The Momo Store also has small items you can ------- as souvenirs. (A) replace (B) borrow purchase (D) sell

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英語 高校生

この選択であっているのかそしてなぜほかの答えではダメなのか教えていただきたいです。

Education Text Completion Select the best answer to complete the text. Then choose the letter (A), (B), (C), or (D). Questions 9-12 refer to the following web page. Part 5 Incomplete Sentences Select the best answer to complete the sentence. Then choose the letter (A), (B), (C), or (D). 1. Before ------- Japan, all international students must get a student visa. (A) enter (B) entering (C) to enter (D) have entered ------- in psychology in university, but now he is an artist. 2. He A majored (A) hers (B) studied (B) she 3. Mr. Toda helped Cathy describe 4. It has been 15 years since I graduated (A) on (B) in 5. Library accounts are automatically created, so no ------- LVU Campus Tours The students of Las Vegas University are at the heart of the LVU experience, 9. tour our campus, meet LVU students, and have them guide you on a campus tour. You can enjoy a candid conversation with 10. students, ask them about classes, housing, Las Vegas, online student support, and more. 11. Doing this will hopefully give you the best idea of what LVU life would be like for you. The two-hour campus tour allows you to experience firsthand everything you need to know. Click here for your guided tour. (C) researched (D) took research plan. (C) her (D) herself ------- university. (C) at (D) from registration is 9. (A) so 10. (A) now (B) then (B) modern (C) initials (D) initialed 12. (C) also (C) latest (D) and (D) current necessary. (A) initially (B) initial 6. I'm happy to have this ------- to study with such great professors. (A) notice (B) benefit (C) factor 7. Statistics is a ------- class for second-year students. (A) require (B) required (C) requiring 8. The geologists plan to study the soil from the mountains Dopportunity (D) requires ------- Canberra. 11. A We will match you with a guide based on your interests and goals. (B) Feel free to ask about other universities found in the area. (C) Take the time to learn more about the city of Las Vegas online. (D) Please let us know the kind of person you were in high school. 12. (A) arrange (B) to arrange Carranging (D) arrangement (A) out (B) next (C) onto (D) around

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