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

Algebra ->  Graphs -> 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      Log On


   

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(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The slope in general would be
the steps to simplify not shown here,...

m=%28x%5E4%2B2x%5E3%2B3x%5E2-2x-1%29%2F%28x%5E2%2Bx%2B1%29%5E2.

For the point whose x coordinate is 1,
f%281%29=y=%281%5E3%2B1%29%2F%281%5E2%2B1%2B1%29
f%281%29=y=2%2F4=1%2F2
the point being (1, 1/2).

The slope for x=1, according to the formula found for m=df%2Fdx,
is %281%5E3%2B2%2A1%5E3%2B3%2A1%5E2-2%2A1-1%29%2F%282%5E2%29
3%2F4,

Then if using point-slope linear equation form,
highlight%28y-1%2F2=%283%2F4%29%28x-1%29%29
or put into slope-intercept form,
y=%283%2F4%29x-3%2F4%2B1%2F2
y=%283%2F4%29x-3%2F4%2B2%2F4
highlight%28y=%283%2F4%29x-1%2F4%29

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 %28ho%2Adhi-hi%2Adho%29%2F%28ho%2Aho%29 .