Find an equation of the tangent line to the curve at the given point. y=4 x-3 x^2,(2,-4)

Name: Problem 5, Chapter 2: Calculus
Uploaded: 2017-11-21T03:11:15-08:00
Duration: 3 min 17 s
Channel: Daniel Jaimes
Description: Find an equation of the tangent line to the curve at the given point. y=4 x-3 x^2,(2,-4)

step 1 this problem of five of the Stuart Calculus eighth edition section two point seven by the equati

Find an equation of the tangent line to the curve at the...

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Key Concepts

Differentiation of Polynomial Functions

Differentiation is a fundamental process in calculus used to find the derivative of functions, including polynomials. For polynomials, this typically involves applying the power rule, which simplifies the calculation of rates of change.

Point-Slope Form

The point-slope form is a method for writing the equation of a line when a point on the line and the slope are known. It is expressed as y ? y? = m(x ? x?), making it a convenient tool for formulating the equation of a tangent line.

Derivative

The derivative of a function represents the instantaneous rate of change of the function with respect to its variable. It is computed using limits and provides the slope of the tangent line to the curve at any given point.

Tangent Line

A tangent line to a curve at a specific point is a line that touches the curve at that point and has the same slope as the curve does there. It is often used to approximate the value of the function near that point.

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