In Exercises 47-50, choose the correct answer. You may use a...

In Exercises $47-50,$ choose the correct answer. You may use a calculator. Multiple Choice If $f(x)=x^{3},$ find the derivative of $f$ at $x=2 .$ $$ \begin{array}{llll}{\text { (A) } 3} & {\text { (B) } 6} & {\text { (C) } 12} & {\text { (D) } 18} & {\text { (E) Does not exist }}\end{array} $$

In Exercises $47-50,$ choose the correct answer. You may use a calculator.
Multiple Choice If $f(x)=x^{3},$ find the derivative of $f$ at $x=2 .$
$$
\begin{array}{llll}{\text { (A) } 3} & {\text { (B) } 6} & {\text { (C) } 12} & {\text { (D) } 18} & {\text { (E) Does not exist }}\end{array}
$$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Derivative

A derivative represents the rate of change of a function with respect to its variable. It provides a way of understanding how a function behaves and changes at each point, which is foundational in calculus for analyzing motion, growth, and various physical phenomena.

Power Rule

The power rule is a fundamental differentiation technique used in calculus to find the derivative of power functions. It states that for any function of the form f(x) = x^n, the derivative is f'(x) = n*x^(n-1), making it a quick and efficient method for differentiating polynomials.

Evaluation of a Derivative at a Point

Once the derivative of a function is known, it can be evaluated at a specific point to determine the instantaneous rate of change at that location. This process involves substituting the specific value of the variable into the derivative function to obtain a numerical result, providing insight into the behavior of the function at that point.

Transcript

Please give Ace some feedback