Question

Find the equation of the tangent line to the graph of p(x)=-x-3 at x=1.

Answer 1

-1/2x^2 - 3x

Answer 2

How?

Answer 3

the only way to get -x as a derivative is -1/2x^2 and the only way to get -3 as a derivative is -3x

Answer 4

i dont know the specific rule/law/theorem though

Answer 5

I still don't understand.

Answer 6

do you know how to get a derivative going forward

Answer 7

is this really
\[p(x)=-x-3\]?

Answer 8

f'(x) = -x - 3

Answer 9

oooooooooooooh

Answer 10

that is not what it says. it says

Find the equation of the tangent line to the graph of p(x)=-x-3 at x=1.

Answer 11

my bad, sorry, im not that far yet in math then lol

Answer 12

and since that is a line itself, the tangent line is the same as that line

Answer 13

So the answer would be -x-3?

Answer 14

i believe the answer is -1 because the derivative of p(x)= -x-3 is -1

Answer 15

-1 is the slope
for the line you need a point so plug in x=1 in the original equation and then do point slope

Answer 16

if the question is really the one you asked, then you are asked to find the equation of a line tangent to a line

Answer 17

sorry i was so confused before

Answer 18

a rather silly question, but it is the line itself. that is all

Answer 19

so what about this then...Find the equation of the tangent line \to the graph of \[h(x)=2x^3-4x^2 at x=-2\]

Answer 20

now that is a more reasonable question.
1) take the derivative
2) evaluate the derivative at x = -2 to get the slope
3) evaluate the function at x - -2
4) use the point - slope formula

Answer 21

first find the derivative of the equation - 6x^2 - 8x, that is the slope at any given point, plug in -2 for the x value and that is the slope of the line
then, plug in -2 into the original equation, that is the y value of the point (-2,y), use that as your point for point slope

Answer 22

So help me work this out... 1)

Answer 23

and it is 6x^2 -8x, not -6 sorry

Answer 24

6x^2-8x?

Answer 25

yes

Answer 26

then, plug in the -2

Answer 27

okay then 2) 6(-2)^2-8(-2)

Answer 28

you plug in -2 into the orignial equation to get the y-coordinate which is -32. then you find the derivative using the power rule (6x^2-8x) and then plug in x=-2 into the derived equation to get the slope at that particular point. the equation would then be y+32=40(x+2)

Answer 29

24+16

Answer 30

yeah, 40

Answer 31

that is the slope, now plug -2 into the original equation

Answer 32

k

Answer 33

then what?

Answer 34

so now i have -32 and 40

Answer 35

your point to plug in to point slope.... \[y-y _{1} = m(x-x _{1})\] so your point is (-2, -32)
and your slope or m is 40

Answer 36

So plug it in for me?

Answer 37

Please

Answer 38

i dont have a calculator, and most teachers let you leave it as point slope so it is
\[y+32=40(x+2)\]

Answer 39

perfect...thank you