Yahoo 知識+ 將於 2021 年 5 月 4 日 (美國東岸時間) 停止服務,而 Yahoo 知識+ 網站現已轉為僅限瀏覽模式。其他 Yahoo 資產或服務,或你的 Yahoo 帳戶將不會有任何變更。你可以在此服務中心網頁進一步了解 Yahoo 知識+ 停止服務的事宜,以及了解如何下載你的資料。

Critical Points problem of Calculus

Find the critical points and determine the type of critical point:

y = e^x + sinx

1 個解答

  • 小儒
    Lv 5
    1 十年前

    y = e^x + sin x

    y' = e^x + cos x

    For x≧0, we should note that e^x is always greater than cos x, implying y is monotonic , i.e. y has no critical point for x≧0

    For x<0, 0 < e^x < 1, monotonic and -1 < cos x < 1, periodic. Thus y' cuts through x-axis occasionally. So all the solutions for x to the equation e^x + cos x = 0 are the critical points. They are all stationary points.

    (In fact, e^x is so small that can be neglected and y' ≒ cos x. A close estimation to the critical points are x ≒ -pi/2, -3pi/2, -5pi/2 ......)

    Hope the above information helps =)

    By 小儒