Question

Look and see if I am right...
1. Suppose the function f of x equals 4 divided by x
a) Use the definition of the derivative to show that f ' (-2) = -1.
b) Write an equation for the line tangent to the graph of f at x = -2.
f(x) = 4/x = 4*x^(-1)
a. f ' (x) = -4*x^(-2)
f'(x) = -4*(-2)^(-2)=-1

Answer 1

b) At x = -2, f ' (-2) = slope
: y - y_1 = slope * (x - x_1) where [x_1, y_1] = [-2, f(-2)]

Answer 2

Therefore you plug in the values:
\[y-f(-2)=-1\times(x-(-2))\]

Answer 3

For which part?

Answer 4

for part b

Answer 5

okay did part a look alright?

Answer 6

yep :D

Answer 7

okay so what do I plug into the second one?

Answer 8

what do you mean the second one

Answer 9

part b

Answer 10

you plug in (x_1,y_1)=(-2,f(-2)) to y-y_1=slope(x-x_1)

Answer 11

That gives you:
\[y-f(-2)=-1\times(x-(-2))\]

Answer 12

and that is all I have to do?

Answer 13

ofc :)

Answer 14

well you need to simplify it

Answer 15

-x+2?

Answer 16

y-f(-2)=-(x+2)
y-4/(-2)=-x-2
y+2=-x-2
x+y+4=0

Answer 17

sorry i meant -x-2

Answer 18

okay awesome. Thank you!