Limit Definition Of A Derivative

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| By Garrettvb1
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Garrettvb1
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Quizzes Created: 1 | Total Attempts: 440
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Derivative Quizzes & Trivia

This quiz will test your knowledge of the limit definition of a derivative. You are to answer the questions to the best of your ability, and submit your answers no later than one week after the first lesson on the limit definition of a derivative.


Questions and Answers
  • 1. 

    What is the formula for finding the derivative of a function over it's range?

  • 2. 

    What is the formula for finding the derivative of a function at a point?

  • 3. 

    What is the derivative of x^2?

    • A.

      X^2

    • B.

      2x

    • C.

      2x^2

    Correct Answer
    B. 2x
    Explanation
    The derivative of a function represents its rate of change at any given point. In this case, the function is x^2. To find its derivative, we can apply the power rule of differentiation. According to the power rule, when we differentiate x^n, the result is n*x^(n-1). Applying this rule to x^2, we get 2*x^(2-1), which simplifies to 2x. Therefore, the derivative of x^2 is 2x.

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  • 4. 

    What is the derivative of x^4+3 at x=2?

    • A.

      32

    • B.

      4

    • C.

      12

    • D.

      3

    Correct Answer
    A. 32
    Explanation
    The derivative of a function represents the rate of change of the function at a given point. To find the derivative of x^4+3, we can apply the power rule, which states that the derivative of x^n is equal to n*x^(n-1). Applying this rule, the derivative of x^4 is 4*x^(4-1) = 4*x^3. Since we are interested in finding the derivative at x=2, we substitute x=2 into the derivative expression: 4*2^3 = 4*8 = 32. Therefore, the derivative of x^4+3 at x=2 is 32.

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  • 5. 

    Set up the limit to find the derivative of x^6+x^4+(x+3)^(1/2).  DO NOT SOLVE.

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  • Current Version
  • Mar 20, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 15, 2010
    Quiz Created by
    Garrettvb1
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