Question

Finding the Slope of a Graph In Exercises $31-38$ , find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. $$y=2 x^{4}-3$$ (1,-1)

Name: Problem 34, Chapter 2: Calculus of a Single Variable
Uploaded: 2019-07-04T14:45:59-08:00
Duration: 1 min 22 s
Channel: Ashley Boni
Description: Finding the Slope of a Graph In Exercises 31-38 , find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. y=2 x^4-3 (1,-1)

   Finding the Slope of a Graph In Exercises $31-38$ , find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.
$$y=2 x^{4}-3$$ (1,-1)

Calculus of a Single Variable

Ron Larson 11th Edition

Chapter 2, Problem 34

Instant Answer

Solved by Expert Ashley Boni

07/04/2019

Step 1

The derivative of a function gives us the slope of the function at any given point. The derivative of the function $y=2x^4-3$ is given by the power rule, which states that the derivative of $x^n$ is $nx^{n-1}$. So, the derivative of $y=2x^4-3$ is Show more…

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Finding the Slope of a Graph In Exercises $31-38$ , find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. $$y=2 x^{4}-3$$ (1,-1)

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Key Concepts

Derivative

The derivative is a fundamental concept in calculus that measures the instantaneous rate of change of a function with respect to its independent variable. It provides the slope of the tangent line at any point on the function's graph, indicating how rapidly the function's output is changing at that point.

Tangent Line

The tangent line to a curve at a specific point is a straight line that touches the curve at that point without crossing it. Its slope is equal to the derivative of the function at that point, making it a useful tool for approximating the function locally.

Graphing Utility and Derivative Feature

Many graphing utilities include a derivative feature that automates the process of finding the derivative of a function and evaluating it at any given point. This feature helps in verifying manual calculations by providing a visual representation of the function along with the slope of the tangent line at specific points.

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