Question

Use the limit definition to compute f'(a):
f(x) = 1x + x−1, a = 4

Find an equation of the tangent line using variables y and x.

Answer 1

Sorry! The equation is f(x) = 1x + x^(−1)

Answer 2

aka
\[x+\frac{1}{x}\]?

Answer 3

f(x) = 1x + x^−1, a = 4
f '(x)=1+x^-2

f '(4)=1+4^-2=17/16=1.0625

Answer 4

Satellite: Yes.

It's 15/16 actually. I almost understand why, but I'm still having some trouble with the algebra.

Answer 5

Use the power rule.
\[f(x)=x+x^-1, a=4\]
\[f \prime(x)=1-1x ^{-2}\]
\[f\prime(4)=1-(1/4^2)\]=(15/16)