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est 1 This Question 6 pts This Test 100 pts Time Remaining: 01:24:19 Find the equation of the tangent line to the graph of the function at the given point. at X The equation for the line tangent to fix at x (Type an equation using x and y as the variables.)

Solution

Equation of tangent to f(x) = 1/x at x=-4

first find point ( x, f(x) )

So,f(x) = -1/4

So, point ----> ( -4 , -1/4)

slope of tangent is found by df/dx = -1/x^2

slope of tangent = -1/x^2 at x= -4

m = - 1/4^2 = -1/16

So, std equation of line for tangent : y =mx +c---> y = -x/16 +c

Find c using ( -4 , -1/4)

-1/4 = -(-4)/16 + c

-1/4 -1/4 = c-----> c = -1/2

y = - x/16 -1/2 ( equation of tangen)