Question

Tangent line equation. (a, f(a)), f(x) = x^2, with a = 2.

Answer 1

there are 2 ways to solve this problem

Answer 2

ok!

Answer 3

1) By using the definition and I forgot abt the other way lol

Answer 4

hahaha , ok, lets use the definition

Answer 5

first :

(a, f(a) ) is going to be :

(2, 4)<-- you'll use these points later to find the equation

we'll have to find the slope first

Answer 6

>_< calculus I lol, alright, remind me, m = limit of that function

Answer 7

f(x) - f(a) = f'(a) . (x - a)

Answer 8

LOL! that's it! find the derivative!

Answer 9

you have f(a) = 4, and a = 2

Answer 10

are you sure that you have to find the derivative? I remember something with limits

Answer 11

\[\ m= lim_{h \rightarrow 0}f(a) - f(a+1)/h\]

that's the equation needed if we want to find the slope using the definition , right?

Answer 12

yeap!

Answer 13

alright! all we have to do is plug in the values we have

Answer 14

hmmm if f(x) = x^2, then f(a) = a^2 , right?

Answer 15

that's correct.

Answer 16

then,\[= \lim_{h \rightarrow 0} (a^2 -a^2-1)/h\]

= -1/h...hmm there's something wrong. h must be canceled

Answer 17

LOL! no no no wait!

Answer 18

\[\lim_{h \rightarrow 0} f(a) - f(a+h)/h \]

that's the right equation LOL! sorry ^^"

Answer 19

np

Answer 20

so you'll get:\[=\lim_{h \rightarrow 0} (a^2 -a^2 -h)/h\]\[=\lim_{h \rightarrow 0} -h/h\]

m = -1

^_^ there we have found m and we have the points (2,4) <-- you know how I got them right?

Answer 21

a = 2, f(a) = (2)^2 = 4

(2,4)

Answer 22

ahhhh

Answer 23

i got it. thanks!

Answer 24

soooooooooooo, we'll use the equation which is :

y -yo = m (x-xo)

y - 4 = = -1(x-2)

^_^ LOL np :)

Answer 25

sorry abt the mess though >_<

Answer 26

np :)

Answer 27

^_^ good luck