Posted by Rudy on Wednesday, December 5, 2012 at 1:29am.
Given the function y=(x^25/x+3), answer the following questions.
a) Find dy/dx. Simplify your answer
b) Find the coordinates of any points on the graph of y where the tangent line is horizontal. Show your work.
c) Are there any points on the graph of y where the tangent line is parallel to the line y=x+7? Explain your answers.

Calculus  Steve, Wednesday, December 5, 2012 at 11:37am
y' = (x^2+6x+5)/(x+3)^2 = (x+1)(x+5)/(x+3)^2
or, you could say y = x3+4/(x+3), so
y' = 1  4/(x+3)^2
so, where is y'=0? x = 1 or 5
where is y'=1? nowhere, since 14/(x+3)^2 < 1 for all x. Note that y has a slant asymptote with slope=1.
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