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Defining the Derivative and Using Derivative Notation

AP Calculus AB· difficulty 3/5

For f(x)=x3f(x) = x^3, evaluate lim⁡h→0(2+h)3−8h\displaystyle\lim_{h\to 0} \dfrac{(2+h)^3 - 8}{h}.

  • A

    1212

    check_circle
  • B

    44

  • C

    88

  • D

    00

Explanation

Expand or recognize: this is f′(2)f'(2) for f(x)=x3f(x) = x^3, i.e. 3⋅22=123 \cdot 2^2 = 12.

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