Christos
  • Christos
Limits, Can you help me find out this specific thing I dont know how to find out http://screencast.com/t/PUvesX4N
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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agent0smith
  • agent0smith
Once you find f'(x), plug in a to get the slope of the line, m. Then you want to get it in the form y=mx+b, by using the fact it passes through the point (a, f(a))
BTaylor
  • BTaylor
Do you know how to take the derivative? If so, then first take the derivative of the function, then evaluate it at the given a -- this is "m", the slope of the tangent line. Now, evaluate the function at the given a. This we'll call "y1" The tangent line is: y-y1 = m (x-a)
Christos
  • Christos
Can please someone tell me what is a slope just so I get the bigger picture of whats going on?

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agent0smith
  • agent0smith
Slope is the steepness of the line, or rate of change. Remember back in algebra, equations y=mx+b have a slope of m.
Christos
  • Christos
@BTaylor what do you mean by "Now, evaluate the function at the given a. " ?
BTaylor
  • BTaylor
so, for number 9, f(x) = 2x^2. The given "a" is 1. So evaluating the function at a means you plug in a for x, and get 2(1)^2, which is 2.
agent0smith
  • agent0smith
That means plug in x=1 (since a=1) into f = 2x^2
BTaylor
  • BTaylor
@agent0smith is right. To visualize this tangent line, click this link: http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=tangent%20line%20to%202x%5E2%20at%20x%3D1
Christos
  • Christos
I got y1 = 0
Christos
  • Christos
y1 = -2
Christos
  • Christos
y1 = 2 :D **
BTaylor
  • BTaylor
the last one is right. y1 = 2.
Christos
  • Christos
so that's the answer?? y1 = 2 and I am done? Nothing else needed?
agent0smith
  • agent0smith
No... did you find the slope?
Christos
  • Christos
its 4
BTaylor
  • BTaylor
yes. because the derivative is 4x, evaluated at x=1 gives you 4(1) =4
agent0smith
  • agent0smith
So then put it in point-slope form: y-y1 = m (x-x1) where x1 = 1, y1= 2
Christos
  • Christos
yea
Christos
  • Christos
I did all that and I got y1 = 2 in the end, I am done ?
agent0smith
  • agent0smith
Wait, no, where is your x going? y-y1 = m (x-a) y - 2 = 4(x-1)
Christos
  • Christos
x-1 = 0
Christos
  • Christos
x = 1
agent0smith
  • agent0smith
x is x.
agent0smith
  • agent0smith
a is 1.
Christos
  • Christos
then why y is not y too and had to be replaced
agent0smith
  • agent0smith
y is y. y-2 = 4 (x-1)
agent0smith
  • agent0smith
You're using point slope form to write the equation of a line: http://www.purplemath.com/modules/strtlneq2.htm
Christos
  • Christos
Nice! I see now! Thank you both! I wish I could give more medals!
agent0smith
  • agent0smith
Your line has a slope of m=4, and passes through the point (1, 2) then you just plug it into the point slope formula.
Christos
  • Christos
oh i see
agent0smith
  • agent0smith
And again, this is what you have found: http://www.wolframalpha.com/input/?t=crmtb01&f=ob&i=tangent%20line%20to%202x%5E2%20at%20x%3D1
Christos
  • Christos
yes

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