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Tracenoxus

Guest

Tangent Line Problems Help

I need help.

f(x)=2/(x+1), (0,2)

Find an equation of the tangent line to the graph of f at the give point.

I need to do this in the limit form. You know, lim [f(c+h)-f(c)]/h
                                                                 h->0
I totally forgot how to do this when it is a hyperbola

sk

Member

Registered: 2006-08-04

Posts: 19

Re: Tangent Line Problems Help

Given function is f(x) = 2/(x+1).
We need to find the equation of the tangent at (0, 2)

Step 1: Find the derivative of the function f(x) = 2/(x + 1)
f1(x) = -2/(x+1)^2 = -2/(x^2+2x+1)
Step 2: Now, substitute the x value from the given point in the derivative of f(x) and find the slope of the required line.
==> -2/(0 + 0 + 1)
f1(x) = -2.
==> Slope = -2.
Step 3: Now, we have the slope as -2 and the point as (0, 2).
then the equation is given by y - y1 = m(x-x1)
y -2 = -2(x-0)
y - 2 = -2x
==> 2x + y - 2 = 0 is the required equation of the tangent.