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3.2-bo'lim : Hosilaning talqini

1 va 2-masalalar uchun \(f\left( x \right)\) funksiya grafigidan foydalaning, \(a\) ning berilgan qiymatlari uchun \(f'\left( a \right)\) qiymatini baholang.

    1. \(a = - 2\)
    2. \(a = 3\)
    The graph of \(f\left( x \right)\) on \( - 3 \le x \le 4\). It is a parabola shaped curve that comes down from approximately \(\left( { - 3,6} \right)\), crosses the x-axis at about \(x = - 1.8\), reaches its lowest point at approximately \(\left( { - 0.2, - 2.5} \right)\) and then increases, crossing the x-axis at \(x = 2\) and reaching approximately \(\left( {4,3.5} \right)\) at the right end.
    Yechim
    1. \(a = 1\)
    2. \(a = 4\)
    The graph of \(f\left( x \right)\) on \(0 \le x \le 5\). The graph starts at approximately \(\left( {0, - 5} \right)\) and increases the whole way, slowly at first and then much more steeply. It crosses the x-axis at about \(x = 3.3\) and reaches approximately \(\left( {5,7} \right)\) at the right end.
    Yechim

3 va 4-masalalar uchun berilgan shartlarni qanoatlantiradigan funksiya grafigini chizing.

  1. \(f\left( 1 \right) = 3\), \(f'\left( 1 \right) = 1\), \(f\left( 4 \right) = 5\), \(f'\left( 4 \right) = - 2\) Yechim
  2. \(f\left( { - 3} \right) = 5\), \(f'\left( { - 3} \right) = - 2\), \(f\left( 1 \right) = 2\), \(f'\left( 1 \right) = 0\), \(f\left( 4 \right) = - 2\), \(f'\left( 4 \right) = - 3\) Yechim

5 va 6-masalalar uchun \(f\left( x \right)\) funksiya grafigi berilgan. Bundan \(f'\left( x \right)\) lotinining grafigini chizish uchun foydalaning.

  1. The graph of \(f\left( x \right)\) on \( - 3 \le x \le 6\). Starting at approximately \(\left( { - 3,4} \right)\) the graph rises to a peak at approximately \(\left( { - 2,7} \right)\), then decreases to a valley at approximately \(\left( {1,2} \right)\), then increases to a peak at approximately \(\left( {5,12.5} \right)\) and finally decreases a little to approximately \(\left( {6,9} \right)\) at the right end.
    Yechim
  2. The graph of \(f\left( x \right)\) on \( - 4 \le x \le 4\). It is made up of three straight line segments. The first runs down from \(\left( { - 4,5} \right)\) to a corner at \(\left( { - 1,2} \right)\), the second runs up from there to a corner at \(\left( {2,4} \right)\), and the third runs back down from there to \(\left( {4,0} \right)\).
    Yechim
  3. \(W\left( z \right) = 4{z^2} - 9z\) funksiyasi haqida quyidagi savollarga javob bering.
    1. \(z = - 1\) da funktsiya ortib bormoqdami yoki kamayyaptimi?
    2. \(z = 2\) da funktsiya ortib bormoqdami yoki kamayyaptimi?
    3. Funktsiya hech qachon o'zgarishni to'xtatadimi? Ha bo'lsa, \(z\) ning qaysi qiymati(lar)ida funktsiya o'zgarishni to'xtatadi?
    Yechim
  4. \(x = 8\) da \(f\left( x \right) = 3 - 14x\) ga teguvchi chiziq tenglamasi qanday? Yechim
  5. Ob'ektning istalgan vaqtda \(t\) pozitsiyasi \(\displaystyle s\left( t \right) = \frac{{t + 1}}{{t + 4}}\) tomonidan beriladi.
    1. Ob'ektning istalgan vaqtda tezligini aniqlang \(t\).
    2. Ob'ekt hech qachon harakatni to'xtatadimi? Ha bo'lsa, ob'ekt qaysi vaqtda (lar)da harakatni to'xtatadi?
    Yechim
  6. \(\displaystyle x = \frac{1}{2}\) da \(\displaystyle f\left( x \right) = \frac{5}{x}\) ga teguvchi chiziqning tenglamasi qanday? Yechim
  7. \(g\left( x \right) = {x^3} - 2{x^2} + x - 1\) funktsiyasi qayerda o'zgarmasligini aniqlang. Yechim
  8. \(Z\left( t \right) = \sqrt {3t - 4} \) funksiyasi berilgan nuqtalarda ortishi yoki kamayishini aniqlang.
    1. \(t = 5\)
    2. \(t = 10\)
    3. \(t = 300\)
    Yechim
  9. \(0 \le t \le 6\) uchun idishdagi suv hajmi \(Q\left( t \right) = 10 + 5t - {t^2}\) tomonidan berilgan deylik.
    1. \(t = 0\) da suv hajmi ortib bormoqdami yoki kamayyaptimi?
    2. \(t = 6\) da suv hajmi ortib bormoqdami yoki kamayyaptimi?
    3. Suv hajmi hech qachon o'zgarmaydimi? Ha bo'lsa, ovoz balandligi qaysi paytlarda o'zgarishni to'xtatadi?
    Yechim