Question

(a) Find the equation of the tangent line to
f(x) = x3 − 3x2 + 2x − 2
at
x = 2.

Answer 1

what does y= ?

Answer 2

im confused on what im supposed to do?
i understand to find the tangent line i must find the derivative. right?

Answer 3

find derivative

Answer 4

that will give you slope

Answer 5

f ' (x)=3x^2-6x+2

Answer 6

\[f \prime (x) = 3x ^{2}-6x+2\]

Answer 7

at x=2
find its value ???

Answer 8

f ' (2) =????
replace x by 2 here

Answer 9

2

Answer 10

\[f \prime (2) = 2\]

Answer 11

\[f \prime (2) = 3(2)^{2}-6(2)+2 = 12-12+2 = 2\]

Answer 12

right?

Answer 13

now this is slope of the tangent

Answer 14

so what is Y= ?

Answer 15

does* y= ?

Answer 16

now we have x=2 we need valur of y so that we can find the point from which it will pass

Answer 17

find f(2)

Answer 18

that is m=slope

Answer 19

y=mx+c

Answer 20

so y-y1 = m(x-x1) ?

Answer 21

or y - f(a)=m(x-a)

Answer 22

so to find y put x=2 in f(x) equation which is in start

Answer 23

yeah but we need y1

Answer 24

yea but you need you actual function value at 2 so just plug 2 into the original

Answer 25

oh yeah

Answer 26

which we will get when we calculate f(2)

Answer 27

you got it ??

Answer 28

but we dont have m do we?
oh yeah m=2, and x=2

Answer 29

yea m = f'(x) derivative is your slope

Answer 30

y=-2

Answer 31

then plug in my factors and get y?

Answer 32

so using the format of y - y1 = m(x - x1) you get?

Answer 33

\[y-(-2)= 2(x-2)\]

Answer 34

yes that is you tangent line equation

Answer 35

y=2x-6

Answer 36

f(x) = x3 − 3x2 + 2x − 2
find f(2) here

Answer 37

f(x)=x3-3x2=2x-2
find f(2) from here

Answer 38

she has that it is -2

Answer 39

so my steps are=
1. find m by finding the derivative
2. find y by plugging x into f(x)
3. set my equation y-y1=m(x-x1) and plug in my factors

Answer 40

correct

Answer 41

yeppp

Answer 42

you got the concept

Answer 43

to find M i plug x=2 into f1(x) right?

Answer 44

that will give me the slope at x=2 ?

Answer 45

yes you plut your x-value given into your derivative formula

Answer 46

plug*

Answer 47

no no no
slope we calculated by derivative

Answer 48

yyaaayyy i think i'm finally getting the hang of this lol

Answer 49

we have to find value of y corresponding to x=2

Answer 50

yea F(prime)X = derivative

Answer 51

f(x) give value of y corrresponding to x

Answer 52

basic format of these problems if your given that x equals a value

1. find f'(x)
2. find f'(a)
3.find f(a)
4. plug values into y - y1 = m(x - x1)

Answer 53

y=f(2)=2^3-3*2^2+2*2-2

Answer 54

y=f(2)=8-12+4-2=-2
so tangent pass through (2,-2)

Answer 55

and slope = 2

Answer 56

y-(-2)=2(x-2)

Answer 57

thanks

Answer 58

A solution and plot is attached. The calculations and plot are from Mathematica 9.