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. Find the equation of the tangent line to the curve at the po

Question 1009797: 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.
Find the equation of the tangent line to the curve at the point (4,1).

Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
f(x)=(x^3+1)/(x^2+x+1)
f(x) = x^5 + x^4 + x^3 + x^2 + x + 1
When x = 1 y = 6
f'(x) = 5x^4 + 4x^3 + 3x^2 + 2x + 1
f'(1) = 5 + 4 + 3 + 2 + 1
f'(1) = 15 (gradient of tangent)
Using y - b = m(x - a)
y - 6 = 15(x - 1)
y = 15x - 15 + 6
y = 15x - 9
..............
f'(x) = 5x^4 + 4x^3 + 3x^2 + 2x + 1
f'(4) = 1593 (Gradient of tangent)
Using y - b = m(x - a)
y - 1 = 1593(x - 4)
y = 1593x - 6372 + 1
y = 1593 - 6371
..................
Hope this helps :-)
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