Find the equation of the tangent line to ='false' f(x)=(x-3)^6 at the point where x=4.

Question:

Find the equation of the tangent line to {eq}f(x)=(x-3)^6 {/eq} at the point where x=4.

Equation of the Tangent Line:

In order to find the equation of the tangent line to the curve, we will first find the coordinates of the point where the tangent line is to be drawn. By taking the first derivative of the curve at the given point we will find the slope of the tangent line. Using the point-slope form of the equation of the line we can find the equation of the tangent line.

Answer and Explanation:

{eq}f(x)=(x-3)^6 {/eq} at {eq}x=4 {/eq}

When {eq}x=4 {/eq}

{eq}f(x)=y=1 {/eq}

Point{eq}=(4,1) {/eq}

The slope of the tangent line is given by:

{eq}f^{'}(x)=6(x-3) \\f^{'}(x)]_{x=4}=6(4-3)=6 {/eq}

Using the point-slope form of the equation of the tangent line is:

{eq}y-1=6(x-4) \\y-1=6x-24 \\6x-y-23=0 {/eq}


Learn more about this topic:

Tangent Line: Definition & Equation

from NY Regents Exam - Geometry: Tutoring Solution

Chapter 1 / Lesson 11
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