SOLUTION: Find an equation of the tangent line to the graph of f(x)=(x^3+1)/(x^2+x+1) at the point whose x-coordinate is 1

Algebra ->  Equations -> SOLUTION: Find an equation of the tangent line to the graph of f(x)=(x^3+1)/(x^2+x+1) at the point whose x-coordinate is 1       Log On


   

Question 1005663: Find an equation of the tangent line to the graph of
f(x)=(x^3+1)/(x^2+x+1) at the point whose x-coordinate is 1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The slope of the tangent line is equal to the value of the derivative at that point.
So first find the derivative using the quotient rule.

I won't bother to simplify since we're doing an evaluation,
So when, x=1,

m=%283%283%29-3%282%29%29%2F%283%29%5E2
m=%289-6%29%2F9
m=1%2F3
So then find the value of the function at x=1
y=%281%5E3%2B1%29%2F%281%5E2%2B1%2B1%29=2%2F3
Use the point-slope form of a line,
y-2%2F3=%281%2F3%29%28x-1%29
y-2%2F3=%281%2F3%29x-1%2F3
y=%281%2F3%29x%2B1%2F3
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