Chapter 3: Applications of Differentiation
Section 3.3: Taylor Polynomials
At x=3, obtain the equation of the line tangent to the graph of fx=lnx2+3 x+2.
Tools≻Load Package: Student Calculus 1
Context Panel: Assign Function
fx=lnx2+3 x+2→assign as functionf
Obtain the equation of the tangent line from the degree-1 Taylor polynomial
Context Panel: Tutors≻Taylor Approximation
fx→Taylor approximation tutor
Set Degree = 1
Figure 3.3.4(a) is an image of the Taylor Approximation tutor in which P1x, the Taylor polynomial of degree 1, determines the equation of the tangent line in the form y=P1x.
tutor will appear with x=3 and the Degree set to the default 4.
Figure 3.3.4(a) Taylor Approximation tutor
Obtain the equation of the tangent line from first principles
Using the point-slope form, type the equation of the tangent line.
Press the Enter key.
Of course, the degree-1 Taylor polynomial could also have been obtained from the Series option in the Context Panel.
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