   Chapter 3.6, Problem 33E

Chapter
Section
Textbook Problem

Find an equation of the tangent line to the curve at the given point.y = ln(x2 – 3x + 1), (3. 0)

To determine

To find: The equation of the tangent line to the curve at the point.

Explanation

Given:

The equation is y=ln(x23x+1).

The point is (3,0).

Formula used:

The equation of the tangent line at (x1,y1) is, yy1=m(xx1) (1)

where, m is the slope of the tangent line at (x1,y1) and m=dydx|x=x1.

Calculation:

The derivative of y is dydx, which is obtained as follows,

dydx=ddx(y)=ddx(ln(x23x+1))

Let u=x23x+1 and use formula ddx(lnu)=1uddu(u),

dydx=1x23x+1ddx(x23x+1)=1x23x+1(ddx(x2)ddx(3x)+ddx(1))=1x23x+1(2x213(1x11)+0

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