Question

find tangent to witch of agnesi
y= 8/(4+x^2)
at point (2,1)

Answer 1

did you find the derivative?

Answer 2

\[\frac{d}{dx}\frac{1}{f(x)}=\frac{-f'(x)}{f^2(x)}\] is a start

Answer 3

would the derivative be
y= (-16x)/(x^2+4)^2

Answer 4

yes, looks good

Answer 5

how to i proceed?

Answer 6

find the slope by taking \(f'(2)\) then use the point slope formula for the equation of the line

Answer 7

so would it be
y=1/2x

Answer 8

i don't know i didn't do it, but i can check

Answer 9

slope should be negative though

Answer 10

i get a slope of \(-\frac{1}{2}\) and the line as \(y=-\frac{1}{2}x+2\)

Answer 11

how do i make the tangent of that line at (2,1)???

Answer 12

i used \(y-y_1=m(x-x_1)\) with \(m=-\frac{1}{2},x_1=2,y_1=1\)

Answer 13

when i graphed it though, the tangent was at a point 2, 7 or something strange like that