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Derivatives Practice Questions

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Updated on Oct 1, 2011

To review these concepts, go to Derivatives Study Guide.

Derivatives Practice Questions

  1. Find the derivative of f(x) = 8x + 2.
  2. If h(x) = x2 + 5, then what is h'(x)?
  3. Find the derivative of g(x) = 10.
  4. What is the derivative of g(x) = 3 –5x?
  5. Find the derivative of f(x) = 3√x.
  6. If k(x) = x3, then what is k'(x)?
  7. Find the slope of f(x) = 3x2 + x at x = 2.
  8. Where does the graph of g(x) = x2 – 4x + 1 have a slope of 0?
  9. Find the equation of the tangent line to h(x) =1 – x2 at (2,–3).
  10. What is the equation of the tangent line of k(x) = 5x2 + 2x at x= 1?

Solutions

  1. Thus, at x = 2, the slope is f'(2) = 13
  2. Thus, there is a slope of zero when g'(x) = 2x – 4 = 0, This happens when x = 2,
  3. The slope at (2,–3) is h'(2) = –4, so the equation of the tangent line is y = –4(x – 2) – 3 = –4x + 5.
  4. The y value at x = 1 is k (1) = 7.The slope at x = 1 is k'(1) = 12. The equation of the tangent line is y = 12(x– 1) + 7 = 12x – 5.
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