The curve y = 1/(1 + x^2) is called a witch of Maria Agnesi. Find an equation of the tangent line to this curve at the point (1,1/2)

Answer 1

y' = -2(1+x^2)^-3

y'(1) = 2/8 = 1/4 = slope of tangent line at (1,1/2)

now use the point slope formula to get the equation of the tangent line at (1,1/2) with m= 1/4

y-1/2 = (1/4)(x-1)

simplify if you want, eliminate the fraction, multiply by 4 on both sides

4y-2 = x-1, rearrange terms, combine constant terms

x-4y = -1