Limit Definition Of A Derivative

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| By Garrettvb1

Garrettvb1

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Quizzes Created: 1 | Total Attempts: 459

Questions: 5 | Attempts: 459 | Updated: Mar 20, 2023

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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. 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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1
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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

Limit Definition Of A Derivative

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

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

What is the derivative of x^2?

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

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