Find the tangent line approximation to 1/x when x=1

Question

How do i find tangent line approximations??? my prof hasn't gone over this and i don't understand how to do it.

Answer 1

y = 1/x
dy/dx = -1/x^2 = slope
at x = 1, slope = -1/1^2 = -1
find the line with that slope through that point (1,1)
1 = -1 *1 + b
b = 2
so line
y = -x + 2

Answer 2

The function is 1/x. There are a number of approximations, but I suspect you are using this one...

f(x+h)-f(x) / h

(1/(x+h)-1/x )/ h

so let h be some small increment, say .05

(1/1.05 - 1/1)/.05= you do it, that is the slope of the tangent line approximation.

Answer 3

thanks!!