Find the equation of the line tangent to y = –x2 + 3x + 8 at x = 2.

- anonymous

Find the equation of the line tangent to y = –x2 + 3x + 8 at x = 2.

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- anonymous

@dan815 could you help me?

- anonymous

the derivative formula that I got is f'(x)= -6x+1

- anonymous

but none of the answers match my answer

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## More answers

- anonymous

Find the equation of the line tangent to y = –x2 + 3x + 8 at x = 2.
y = –2x + 2
y = –x + 12
y = –x + 2
y = –2x – 12

- dan815

|dw:1436827395674:dw|

- dan815

|dw:1436827520119:dw|

- dan815

y = –x + 12

- anonymous

is it 26

- anonymous

could you explain me how you got that answer

- anonymous

@dan815

- dan815

did you get the derivative function right

- anonymous

yes, because when I plug the value of 2 into my formula I get -1, which you presented me that it was correct, but I don't know how you got that formula

- dan815

f'(x)= -6x+1
you said you got this, something wrong there

- dan815

you have to differentiate term by term

- anonymous

never mind I got -2x+3

- dan815

okay

- dan815

now you have a slope, then you find a point that belongs on this tangent line

- anonymous

but that doesn't have anything in common to the other answers

- anonymous

how?

- dan815

|dw:1436828112090:dw|

- dan815

we know the x coordinate of the point,

- dan815

now we find the y coordinate of the point and its part of the parabola so

- dan815

y(2) = ?

- dan815

|dw:1436828189830:dw|

- anonymous

do we plug it into the original formula or the derivate one?

- dan815

we have the slope there, now we need to find the y coordinate then you will have a point and a slope and you figure out the equation of the line

- dan815

the derivative formula only tells you the slope at every x value

- dan815

we want to know the actual y point

- anonymous

so which formula could I use to find the y value?

- dan815

think about it

- dan815

the tangent line intersects one point on the parabola, at x=2 and y is something, we can always find the y value for every x value on a parabola how?

- anonymous

maximum

- anonymous

wait no, OMG I feel so ignorant.

- dan815

y = –x^2 + 3x + 8
this equation of parabola

- dan815

it gives you a y value for every x value

- dan815

we know there is an intersection at x=2 so we have to see the y value there

- dan815

y = –x^2 + 3x + 8
y=-2^2+3*2+8 = 10

- dan815

x=2,y=10
(2,10)|dw:1436828495281:dw|

- anonymous

I got 10

- anonymous

yes,

- dan815

now u have a point at the slope of the tangent line through that point

- dan815

can you solve the equation of the line from here

- dan815

y=mx+b
m=-1
lets plug in our point to see what b or the y intercept must be
10=-1*2+b
b=

- anonymous

9

- dan815

10=-1*2+b
10=-2+b
b=10+2=12

- anonymous

Oh i see I thought it was a 1 to the second power

- dan815

this is the equation of a line
y=mx+b

- anonymous

yeah, OMG I got it. Thank you so much. Could you help me with one more and thats it?

- dan815

yeah sure

- anonymous

##### 1 Attachment

- anonymous

I already found that C actually has the value, but I don't know how to solve A nor B

- anonymous

@dan815

- anonymous

@phi

- dan815

|dw:1436829534343:dw|

- dan815

this is the definition of a derivative

- dan815

it is the equation to find the slope of a tangent line at x

- dan815

it arises from taking a secant line where the points are getting closer and closer, lim h--->0

- dan815

for example take a look at any function f(x)

- dan815

|dw:1436829711928:dw|

- dan815

suppose you want to find the derivative at that point x for this function, you can begin to approximate by taking points close to that value because that is a close linear approximation

- dan815

|dw:1436829768720:dw|

- anonymous

okay, I see. I got 7 as the slope of the function

- anonymous

at x=2

- dan815

|dw:1436829791039:dw|

- dan815

if we keep making h smaller and smaller then the point is close and closer to the actual tangent slope

- anonymous

which is 7 right?

- dan815

|dw:1436829918175:dw|

- dan815

well my work is done as long you understand how a derivative comes

- dan815

its from this very simple concept, the slope of the tangent line at some point

- anonymous

okay than you, I understood the secant and tangent line more.

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