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Determine the function f satisfying the given conditions F'''(X)=2 F''(0)=3 F'(0)=2 F(0)=5 F(X)=__X^3+___X^2+___X+____?

3 Answers

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  • Alan
    Lv 7
    4 years ago

    First, label the blanks a -d

    F(x) = ax^3 + bx^2 + cx + d

    F(0) = 5

    F(0) = 0 + 0 + 0 +0 +d

    d = 5

    F(x) = ax^3 +bx^2 + cx +5

    F"(x) = 3ax^2 + 2bx + c

    F'(0) = 0 + 0 + c = 2

    c = 2

    F''(x) = 6ax + 2b

    F""(0) = 3

    2b = 3

    b = 3/2

    F'''(x) = 6a = 2

    a = 2/6 = 1/3

    ======= the answer

    F(X) = (1/3)x^3 + (3/2)x^2 + 2x + 5

    === checking answer

    F(0) = (1/3)0^3 + (3/2)0^2 + 2*0 + 5 = 5 (checks)

    F'(0) = x^2+ 3x + 2 = 0^2 + 3*0 + 2 = 2 (checks)

    F''(0) = 2x +3 = 2* 0 + 3 = 3 (checks)

    F""(X) = 2 (checks)

  • alex
    Lv 7
    4 years ago

    integrate few times ---->F(X)=(1/3)X^3+(3/2)X^2+2X+5

  • ted s
    Lv 7
    4 years ago

    2 ---> 2x + 3 ---> x² + 3x + 2 ---> x³ / 3 + 3 x² / 2 + 2x + 5

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