Hi there!
In my bygone consulting jobs, I have helped some small and medium-sized companies start up overseas trades, about 80 percent of which picked up their bottom lines and helped them go on a growth path.
I kept my commitment to my clients as long as I felt comfortable working there with my life and passion, which paid off in helping them grow. However, once the clients had degenerated into typical small-business owners, who usually wanted to have luxurious cars and houses, I withdrew the businesses concerned and cut the relationships with them.
My consulting responsibilities were wide-ranging, such as coordinating participation in trade shows, negotiations, and making a deal, and challenging and rewarding; however, I never hesitated to sever a working relationship with my clients when they lost track of their visions.
Energy gravitates towards clear visions. I never commit to spending my precious time helping my clients who don’t have clear pictures.
Coordinating or facilitating a business was one of my talents, so today, let me scrutinize the coordinates in mathematics without any further ado.
Find the coordinates of the vertex of the graph of the quadratic function \(y = -x^{2} + 4ax + 2a\) where \(a\) is a constant, and also the range of values \(a\) such that the quadratic function always has negative values.(Ref: The Mathematics Certification Institute of Japan; slightly changed the numbers of the quadratic function)
Here is my solution to the problem.
First of all, differentiate the quadratic function.
\(y = -x^{2} + 4ax + 2a\)
\(y’ = -2x + 4a = -2(x – 2a)\)
Thus, the coordinates of the vertex become \((2a, 4a^{2} + 2a)\)
Now \(4a^{2} + 2a < 0\), so
\(2a^{2} + a < 0\)
\(a(2a + 1) < 0\)
Therefore, \(-\frac{1}{2} < a < 0\).
When can I reach the vertex of my career?
Stay tuned, and expect to see my next post.
Keep well.
Frank Yoshida
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【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
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