Limit Definition Of A Derivative

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| By Garrettvb1

Garrettvb1

Community Contributor

Quizzes Created: 1 | Total Attempts: 467

| Attempts: 467

2.

What is the derivative of x^4+3 at x=2?
- 32
- 4
- 12
- 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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3.

What is the formula for finding the derivative of a function over it's range?
4.

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