by Guest » Wed Jun 10, 2020 12:40 pm
So you want to find the tangent line to the graph of this function? At what point?
The tangent line to y= f(x), at [tex]x= x_0[/tex], is [tex]y= f'(x_0)(x- x_0)+ f(x_0)[/tex]. Here [tex]f(x)= \frac{6}{x^2+ 3}= 6(x^2+ 3)^{-1}[/tex]. The derivative is [tex]f'(x)= -6(x^2+ 3)^{-2}(2x)= -\frac{12x}{(x^2+ 3)^2}[/tex]. The tangent line, at [tex]x= x_0[/tex], is [tex]y= -\frac{12x_0}{(x_0^2+ 3)^2}(x- x_0)+ \frac{6}{x_0^2+ 3}[/tex].