Limit Definition Of A Derivative
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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. 2xExplanation
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.Rate this question:
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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. 32Explanation
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.Rate this question:
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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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Feb 19, 2025Quiz Edited by
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Oct 15, 2010Quiz Created by
Garrettvb1