Find the slope of the tangent line to y=x^n at the point (1,1) . (a) y=x^-1 (b) y=x^-1 / 3

Name: Problem 3, Chapter 2: Calculus an Applied Approach
Uploaded: 2021-06-13T23:38:03-08:00
Duration: 2 min 21 s
Channel: Lauren Shelton
Description: Find the slope of the tangent line to y=x^n at the point (1,1) . (a) y=x^-1 (b) y=x^-1 / 3

step 1 Okay, so what have we been talking about in this lesson? Well, we've been talking about the powe

Find the slope of the tangent line to y=x^n at the point...

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Key Concepts

Tangent Line

A tangent line to a curve at a specific point is the line that touches the curve only at that point and has the same instantaneous rate of change (slope) as the curve. It is used to approximate the behavior of the function near that point.

Evaluation of the Derivative

Evaluating the derivative at a specific point involves substituting the point's x-value into the derivative function. This computation provides the precise slope of the tangent line at that point, which is essential in understanding the local linear behavior of the function.

Derivative

The derivative is a measure of how a function changes as its input changes. It represents the slope of the tangent line to a function at any given point, and is calculated as the limit of the difference quotient.

Power Rule

The power rule is a basic method in calculus for differentiating functions of the form x^n, where n is any real number. It states that the derivative of x^n is n*x^(n-1), simplifying the process of finding slopes of power functions.

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