How do you find the equation of the tangent line to the graph of the given function #f(x) = - 1/x#; at (3,-1/3)?

Question

How do you find the equation of the tangent line to the graph of the given function  #f(x) = - 1/x#; at (3,-1/3)?

Emilia Aguilar · Accepted Answer

I found: #y=1/9x-2/3# First you need to find the slope #m# of the tangent line; you need to evaluate the derivative of your function: #f'(x)=1/x^2# and then evaluate it at #x=3# #f'(3)=1/9# this will be the slope of the tangent. Now you can use the relationship: #y-y_0=m(x-x_0)# that with your values gives: #y-(-1/3)=1/9(x-3)# Giving: #y=1/9x-2/3#

Paisley Johnson · Answer

undefined To find the equation of the tangent line to the graph of the function f(x) = -1/x at the point (3, -1/3), we can follow these steps:

1. Find the derivative of the function f(x) using the quotient rule. The derivative of f(x) = -1/x is f'(x) = 1/x^2.

2. Substitute the x-coordinate of the given point (3, -1/3) into the derivative to find the slope of the tangent line. f'(3) = 1/3^2 = 1/9.

3. Use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, to write the equation of the tangent line. Plugging in the values, we get y - (-1/3) = (1/9)(x - 3).

4. Simplify the equation to obtain the final form of the tangent line. The equation of the tangent line to the graph of f(x) = -1/x at (3, -1/3) is y + 1/3 = (1/9)(x - 3).