Determine the equation for the line of the function that has

[Guest]

The function: f(x) = [tex]\frac{6}{x^2+3}[/tex]

Had a hard time solving this. Can you solve it too with steps?

[Guest]

*tangent line

[Guest]

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].