Matematika

Pertanyaan

No 1. F"(x)=5
F'(-2)=-7
F(2)=4

2. F"(x) =10x pangkat 4,
F' (-1) =-5
F(0) = 8

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1 Jawaban

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    f' (x) = ∫ f'(x) dx = ∫ 5 dx
    f '(x)= 5x+ c
    f '(-2) = -7
    5(-2) + c = - 7
    -10 + c =- 7c = 3
    f'(x) = 5x  + 3
    f(x)= ∫ f'(x)= ∫ (5x + 3) dx
    f (x) = 5/2 x² + 3x + c
    f(2)= 4
    5/2 (2)² + 3(2)+ c = 4
    10 + 6 + c = 4
    16 + c = 4
    c = -12
    f(x)= 5/2 x² +3x - 12

    f'(x)= ∫ f " (x) dx = ∫ (10x⁴) dx
    f  '(x)= 2x⁵ + c
    f'(-1) = - 5
    -5 = 2(-1)⁵ + c
    -5 = -2 + c
    c = -3
    f '(x)= 2x⁵- 3
    f (x) = ∫ f '(x) dx = ∫ (2x⁵ -3) dx
    f (x) = 1/3 x⁶ - 3x + c
    f(0) = 8
    8 = 1/3 (0) - 3(0) + c
    c = 8
    f(x)= 1/3 x⁶ - 3x + 8

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