Find the equation of the tangent line to f(x) = 1/√(x) at x = 4. Express your answer in both standard and y=mx+b form. Use first principles.

Answer 1

f'(x) = -1/2 x^(-3/2)
so at (4,1/2) the tangent line is

y - 1/2 = -1/16 (x-4)
rearrange that to the desired form.

See the graphs at

www.wolframalpha.com/input?i=plot+y%3D1%2F%E2%88%9Ax%2C+y+%3D+-1%2F16+%28x-4%29+%2B+1%2F2