Estimating Derivatives at a Point Practice

Sample questions

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1. Sample 1difficulty 2/5

   Estimate $f'(2)$ given $f(1.99) = 4.96$, $f(2.01) = 5.04$.

   • A

     $4$

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   • B

     $5$

   • C

     $0.04$

   • D

     $2$

   Why

   $(5.04 - 4.96)/(2.01 - 1.99) = 0.08/0.02 = 4$.

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2. Sample 2difficulty 3/5

   The graph of $f$ is a horizontal line. Then $f'(x)$ equals:

   • A

     $0$

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   • B

     $k$

   • C

     Undefined

   • D

     $1$

   Why

   Constant function has zero derivative everywhere.

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3. Sample 3difficulty 3/5

   If the dashed tangent line has slope $-5/8$ at the marked point, then $f'$ at that point is:

   • A

     $8/5$

   • B

     $0$

   • C

     $5/8$

   • D

     $-5/8$

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   Why

   The slope of the tangent line equals $f'$ at the point of tangency.

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