Hi, there!
I’ve never dreamed of answering integral word problems since I challenged
university entrance examinations. I didn’t dislike mathematics, but it was a
fact that I always put the subject on the back burner.
I might have a preconception against science; mechanical, electric, electro-
nics, mechatronics, and whatnot. The reason must be that automobile and
electronics manufacturers invigorate their product lines with upgraded mo-
dels yearly. Honestly, I have become sick and tired of their substantial pre-
ssure dwelling in work to mass-produce unattractive, stereotypical widgets
indefatigably.
I don’t have the slightest idea why I have come back to mathematics. I might
be intrigued to figure out any mathematical theorem rather than closing my
eyes against the status quo in which Japanese industries entirely devote
themselves to manufacturing such and such widgets.
An old maxim goes, “Mathematics can help unravel mysteries in the univer-
se.” If so, it pays off to give it a try to configure intangible theorems instead
of environmentally unfriendly materialistic products.
That’s one small step for mathematicians, one giant leap for me.
Here comes the word problem today.
Determine \(f(x)\) given that \(f'(x) = 15x^{2} + 6x\), and \(f(–2) = 172\).
Here is my solution to the problem.
\(f(x) = \int f'(x)dx\)
To arrive at a general formula for \(f(x)\), I must integrate the derivative
given in the problem statement.
\(f(x) = \int (15x^{2} + 6x)\)
\(dx = 5x^{3} + 3x^{2} + C\)
Providing \(f(–2) = 172\), I can just plug \(x = –2\) into my answer from
the previous step, set the result equal to \(172\), and solve the resulting
equation for \(C\).
Doing this gives \(172 = f(–2) = – 40 + 12 + C\), so \(C = 200\).
The function is, therefore, \(f(x) = 5x^{3} + 3x^{2} + 200\)
There is a tendency for scientists to focus on practical or useful things
and for people and budgets to coalesce in areas where results can be
achieved immediately. What short-sighted eyes they have!
Unless you can keep believing in invisible things tenaciously, you will not
be able to become a scientifically big shot, especially in mathematics.
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
【グローバルビジネスで役立つ数学】でもっと学習する b＾＾)
【参考図書】『もう一度高校数学』（著者：高橋一雄氏）株式会社日本実業出版社
【レッスン】私のオンライン英語レッスンをご希望の方はこちらをご覧ください。
【コンテント】当サイトで提供する情報はその正確性と最新性の確保に努めていま
すが完全さを保証するものではありません。当サイトの内容に関するいかなる間
違いについても一切の責任を負うものではありません。
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
只今、人気ブログランキングに参加しています。
今日の［実践数学の達人］のランキングは――
