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Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the given point. See Example 5.
y = ln x3; (1, 0)

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Answer:

[tex]y=3x-3[/tex]

Step-by-step explanation:

We are given that

[tex]y=ln x^3[/tex]

Point (1,0)

We have to find the equation of tangent line to the given graph.

Differentiate w.r.t x

[tex]\frac{dy}{dx}=\frac{1}{x^3}\times 3x^2}=\frac{3}{x}[/tex]

[tex]\frac{d(lnx)}{dx}=\frac{1}{x}[/tex]

Substitute x=1

[tex]m=\frac{dy}{dx}=3[/tex]

Slope-point form:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]x_1=1,y_1=0[/tex]

By using this formula

The equation of tangent to the given graph

[tex]y-0=3(x-1)=3x-3[/tex]

[tex]y=3x-3[/tex]

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