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.

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.

anonymous · Answer

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

anonymous · Answer

aka 
$$x+\frac{1}{x}$$?

anonymous · Answer

f(x) = 1x + x^−1, a = 4
f '(x)=1+x^-2
 
f '(4)=1+4^-2=17/16=1.0625

anonymous · Answer

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

precal · Answer

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)