SOLUTION: 1-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. 2-Find the equation of the tangent line to the curve at th

Question 1009964: 1-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.
2-Find the equation of the tangent line to the curve at the point (4,1).

Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The slope in general would be
the steps to simplify not shown here,...

.

For the point whose x coordinate is 1,

the point being (1, 1/2).

The slope for x=1, according to the formula found for ,
is
,

Then if using point-slope linear equation form,

or put into slope-intercept form,

The other question can then be handled much the same, just re-using the formula for the slope and the given point.

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The mnemonic for formula of derivative of a rational function goes as .
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