Question

Find the equation of thre line tangent to the curve y = (x+3)/√x at its point of inflection.

Answer 1

\[y=\frac{x+3}{\sqrt{x}}=\sqrt{x}+\frac{3}{\sqrt{x}}=x^{1/2}+3x^{-1/2}\]\[y'=\frac{1}{2}x^{-1/2}-\frac{3}{2}x^{-3/2}\]\[y''=-\frac{1}{4}x^{-3/2}+\frac{9}{4}x^{-5/2}=-\frac{1}{4}x^{-5/2}(x-9)=0\quad, x=9\]\[x=9\quad\Rightarrow\quad y=4\quad,\quad y'=1/9\]\[\mbox{tangent line: }y-4=\frac{x-9}{9}\]

Answer 2

nikvist i sent 4 questions

Answer 3

ok