Hi, there!
There is almost never a time when we are unaware of vehicles,
even if only subconsciously. Each time we report to work, we
encounter trains and automobiles on which corporate warriors
ride.
Then I ask myself, on behalf of mathematics geeks, at which
speed they usually walk and keep driving cars by maneuvering
their steering wheels.
Today, I give the differential calculation a shot to review its ba-
sic formula.
What is the speed that a vehicle is traveling according to the
equation \(d(t) = 5 – 6t^{2}\) at the eighth second of its journey?
In this instance, space is measured in meters and time in se-
cond.
Before immediately getting down to my solution, I want to re-
mind you of the definition of the derivative.
・Definition of derivative：\(f'(x)=\displaystyle\lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}\)
・Derivative：\(\frac{dy}{dx}=\displaystyle\lim_{\triangle x\rightarrow 0}\frac{\triangle y}{\triangle x}=\displaystyle\lim_{△x\rightarrow 0}\frac{f(x+\triangle x)-f(x)}{\triangle x}\)
Once you have managed to remind the essence of the deriva-
tive, you probably do not need a detailed explanation about
how to estimate. Are you ready to answer?
OK! Here is my solution to the problem.
\(V^{t}_{8} = \displaystyle\lim_{h\rightarrow 0}\frac{5 – 6(8 + h)^{2} – (5 – 6・8^{2})}{h}\)
\(= \displaystyle\lim_{h\rightarrow 0}\frac{-96h – 6h^{2}}{h}\)
\(= \displaystyle\lim_{h\rightarrow 0}\frac{h(-96 – 6h)}{h}\)
\(= -96\frac{m}{s}\)
I am still too immature to have incredible wisdom, but studying
bit by bit, inch by inch, will make me much closer to the stage
that no one has reached, for sure.
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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