anonymous
  • anonymous
Find the equation of the line tangent to y = –x2 + 3x + 8 at x = 2.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@dan815 could you help me?
anonymous
  • anonymous
the derivative formula that I got is f'(x)= -6x+1
anonymous
  • anonymous
but none of the answers match my answer

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More answers

anonymous
  • 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
  • dan815
|dw:1436827395674:dw|
dan815
  • dan815
|dw:1436827520119:dw|
dan815
  • dan815
y = –x + 12
anonymous
  • anonymous
is it 26
anonymous
  • anonymous
could you explain me how you got that answer
anonymous
  • anonymous
@dan815
dan815
  • dan815
did you get the derivative function right
anonymous
  • 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
  • dan815
f'(x)= -6x+1 you said you got this, something wrong there
dan815
  • dan815
you have to differentiate term by term
anonymous
  • anonymous
never mind I got -2x+3
dan815
  • dan815
okay
dan815
  • dan815
now you have a slope, then you find a point that belongs on this tangent line
anonymous
  • anonymous
but that doesn't have anything in common to the other answers
anonymous
  • anonymous
how?
dan815
  • dan815
|dw:1436828112090:dw|
dan815
  • dan815
we know the x coordinate of the point,
dan815
  • dan815
now we find the y coordinate of the point and its part of the parabola so
dan815
  • dan815
y(2) = ?
dan815
  • dan815
|dw:1436828189830:dw|
anonymous
  • anonymous
do we plug it into the original formula or the derivate one?
dan815
  • 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
  • dan815
the derivative formula only tells you the slope at every x value
dan815
  • dan815
we want to know the actual y point
anonymous
  • anonymous
so which formula could I use to find the y value?
dan815
  • dan815
think about it
dan815
  • 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
  • anonymous
maximum
anonymous
  • anonymous
wait no, OMG I feel so ignorant.
dan815
  • dan815
y = –x^2 + 3x + 8 this equation of parabola
dan815
  • dan815
it gives you a y value for every x value
dan815
  • dan815
we know there is an intersection at x=2 so we have to see the y value there
dan815
  • dan815
y = –x^2 + 3x + 8 y=-2^2+3*2+8 = 10
dan815
  • dan815
x=2,y=10 (2,10)|dw:1436828495281:dw|
anonymous
  • anonymous
I got 10
anonymous
  • anonymous
yes,
dan815
  • dan815
now u have a point at the slope of the tangent line through that point
dan815
  • dan815
can you solve the equation of the line from here
dan815
  • 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
  • anonymous
9
dan815
  • dan815
10=-1*2+b 10=-2+b b=10+2=12
anonymous
  • anonymous
Oh i see I thought it was a 1 to the second power
dan815
  • dan815
this is the equation of a line y=mx+b
anonymous
  • anonymous
yeah, OMG I got it. Thank you so much. Could you help me with one more and thats it?
dan815
  • dan815
yeah sure
anonymous
  • anonymous
anonymous
  • anonymous
I already found that C actually has the value, but I don't know how to solve A nor B
anonymous
  • anonymous
@dan815
anonymous
  • anonymous
@phi
dan815
  • dan815
|dw:1436829534343:dw|
dan815
  • dan815
this is the definition of a derivative
dan815
  • dan815
it is the equation to find the slope of a tangent line at x
dan815
  • dan815
it arises from taking a secant line where the points are getting closer and closer, lim h--->0
dan815
  • dan815
for example take a look at any function f(x)
dan815
  • dan815
|dw:1436829711928:dw|
dan815
  • 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
  • dan815
|dw:1436829768720:dw|
anonymous
  • anonymous
okay, I see. I got 7 as the slope of the function
anonymous
  • anonymous
at x=2
dan815
  • dan815
|dw:1436829791039:dw|
dan815
  • dan815
if we keep making h smaller and smaller then the point is close and closer to the actual tangent slope
anonymous
  • anonymous
which is 7 right?
dan815
  • dan815
|dw:1436829918175:dw|
dan815
  • dan815
well my work is done as long you understand how a derivative comes
dan815
  • dan815
its from this very simple concept, the slope of the tangent line at some point
anonymous
  • anonymous
okay than you, I understood the secant and tangent line more.

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