Question

Given that the graph of f(x) passes through the point (9,3) and that the slope of its tangent line at (x,f(x)) is 6x+6, what is f(2)?

Answer 1

plug in x

Answer 2

You doing antiderivatives?

Answer 3

yes i am

Answer 4

so we have to find the antiderivative of 6x+6 first

Answer 5

which is just 6

Answer 6

thats the derivative

Answer 7

antiderivative?

Answer 8

never heard of that before

Answer 9

wait maybe I'm one step ahead of you

Answer 10

@zepdrix

Answer 11

Have you heard of integral?

Answer 12

no

Answer 13

hmmm weird? This is like a problem in my book where I had to find the integral, because the tangent line is kinda like the derivative so we want to find the original function of f

Answer 14

i've heard of the tangent line and derivative, but not antiderivative

Answer 15

hmmmmm? :(

Answer 16

I can teach you

Answer 17

Because that is what we have to do for this problem

Answer 18

that's fine with me. Im also a fast learner

Answer 19

so it should be easy for me to catch on

Answer 20

Okay cool, so if we had the polynomial 3x^2+2x+7 what would the derivative be? Like what steps do you have to do to find the derivative of this?

Answer 21

Multiply the exponent by the whole number and reduce the power by one correct?

Answer 22

yep :D

Answer 23

so it would be 6x+2

Answer 24

Yes well now were doing kinda the opposite, so now we will be adding 1 to our exponent than dividing by the exponent let me show you an example

Answer 25

so it would 3/2x^3+2x^2

Answer 26

hmmmm?

Answer 27

lets do you problem 6x+6

Answer 28

okay

Answer 29

so 6x^2+6?

Answer 30

well we know that when we have like 8x the derivative of that is 8 so what would be the antiderivative for 6

Answer 31

yes the power would be 2 for the first term with the 6 but don't forget to divide by the exponent

Answer 32

so it would be 6x

Answer 33

yes for the second part good, now we just have to fix the first term

Answer 34

you have the right numerator but you need to divide by the exponent

Answer 35

do we divide the exponent before or after we add 1

Answer 36

after always add one first than divide after you add the 1

Answer 37

okay

Answer 38

3x^2+6x

Answer 39

good! now we need to plug in our x value from the point they gave us and equal it to the y value, do you understand?

Answer 40

Into what you just figured out

Answer 41

\[3=3(9)^2+6(9)\]

Answer 42

wait thats wrong

Answer 43

right and oh I'm sorry don't forget to add a c because we don't know if the antiderivative has a constant or not but it could be 0 10 7 and it still would be the derivative that they gave us

Answer 44

That is what we will be trying to figure out what the value of C is

Answer 45

So you had it right it was my fault so you should have
3=3(9)^2+6(9)+c

Answer 46

oh okay

Answer 47

now solve for c

Answer 48

C=294

Answer 49

yes

Answer 50

And now find what the value is when you plug in 2 for that equation

Answer 51

318

Answer 52

is that my answer?

Answer 53

Wait

Answer 54

Shouldn't it be a negative 294 because you want to get c alone so we had 3=297+c so we need to subtract by 297 to get c all alone

Answer 55

yeah your right my mistake

Answer 56

That's okay!

Answer 57

so our answer is going to be -270

Answer 58

I got -280

Answer 59

Nope just kidding I got -270 too :)

Answer 60

:D

Answer 61

:DD lol good job :)

Answer 62

thank you

Answer 63

No problem :)