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Antiderivatives and Indefinite Integrals

AP Calculus AB· difficulty 3/5

x f'(x)=2

If f′(x)=2f'(x) = 2 and f(0)=5f(0) = 5, then f(x)=f(x) =:

  • A

    2x+52x + 5

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  • B

    2x2x

  • C

    x+5x + 5

  • D

    2x2+52x^2 + 5

Explanation

f(x)=∫2 dx=2x+Cf(x) = \int 2\,dx = 2x + C; f(0)=5f(0) = 5 gives C=5C = 5.

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