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Introduction to Derivatives · Ages 17–18

Differentiating Polynomial Functions Practice

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Differentiate each polynomial with respect to x. For the final questions, evaluate the derivative at the given coordinate.

  1. Find f'(x) for f(x) = x^5

  2. Find f'(x) for f(x) = 6x^3

  3. Find f'(x) for f(x) = 3x^2 - 5x + 9

  4. Find f'(x) for f(x) = -2x^4 + 7x^3 - x + 14

  5. Find f'(x) for f(x) = (1/3)x^3 - (1/2)x^2 + 4x - 11

  6. Find the slope of the tangent to f(x) = x^2 - 6x at x = 4

  7. Find the slope of the tangent to f(x) = 2x^3 - 3x^2 + 1 at x = -1

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Differentiating Polynomial Functions Practice

Answer key

  1. Find f'(x) for f(x) = x^5

    f'(x) = 5x^4

  2. Find f'(x) for f(x) = 6x^3

    f'(x) = 18x^2

  3. Find f'(x) for f(x) = 3x^2 - 5x + 9

    f'(x) = 6x - 5

  4. Find f'(x) for f(x) = -2x^4 + 7x^3 - x + 14

    f'(x) = -8x^3 + 21x^2 - 1

  5. Find f'(x) for f(x) = (1/3)x^3 - (1/2)x^2 + 4x - 11

    f'(x) = x^2 - x + 4

  6. Find the slope of the tangent to f(x) = x^2 - 6x at x = 4

    f'(x) = 2x - 6; at x = 4, slope = 2

  7. Find the slope of the tangent to f(x) = 2x^3 - 3x^2 + 1 at x = -1

    f'(x) = 6x^2 - 6x; at x = -1, slope = 6(-1)^2 - 6(-1) = 6 + 6 = 12