Question

Use a linear approximation (or differentials) to estimate the given number:
1/4.002

I'm need help finding the steps

Answer 1

0.25

Answer 2

.... i think you can find that on calculator

Answer 3

what if he didnt want to use the calc

Answer 4

oh sorry. It's my first time using this. i need to find the linear approx of it

Answer 5

I just dont know the steps

Answer 6

thats fine bro.. u cool

Answer 7

then that means he's lazy not saying you are and dayveed it's okay trindawg is just stupid

Answer 8

oops did i say that?

Answer 9

Hint: your function is f(x) = 1/x

you need to find f ' (x) and evaluate f ' (4)

Answer 10

the point (4, 1/4) lies on the graph of f(x) = 1/x

you need to find the equation of the tangent line L(x) at this point

Answer 11

So i got f(x) =1/16

Answer 12

how are you getting that

Answer 13

f'(x) **

Answer 14

f ' (x) is not 1/16

Answer 15

Don't i find f '(x) of 1/x?

Answer 16

which is -1/x^2

Answer 17

so if i plug in x=4 it would make it - 1/16

Answer 18

yes f ' (x) = -1/x^2

so f ' (4) = -1/16

Answer 19

the slope of the tangent line is m = -1/16

Answer 20

the point this tangent line goes through is (4, 1/4)

Answer 21

so would i do y - 1/4 = -1/16(x-4)?

Answer 22

correct

Answer 23

solve for y to determine L(x)

then you can compute L(4.002) to approximate f(4.002)

Answer 24

okay so y = -1/16x + 1/2 right? so i just plug in 4.002 to x and that's my answer?

Answer 25

correct

Answer 26

Oooo wow nevermind i got it. My teacher taught me a different way so i was confused about where you were going. This way makes a lot more sense. thank you!

Answer 27

sure thing