Yahoo Answers: Answers and Comments for TANGENT??????????????????? [Mathematics]
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From Fapre
enUS
Wed, 09 May 2012 13:46:48 +0000
3
Yahoo Answers: Answers and Comments for TANGENT??????????????????? [Mathematics]
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From Wile E.: y = 3x² + 4x + 2
dy/dx = 6x + 4
x = 2
y = 22...
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Thu, 10 May 2012 04:55:45 +0000
y = 3x² + 4x + 2
dy/dx = 6x + 4
x = 2
y = 22
dy/dx = 6(2) + 4
dy/dx = 12 + 4
dy/dx = 16
b = y  [(dy/dx)(x)]
b = 22  [16(2)
b = 22  32
b =  10
Equation of Tangent Line:
y = 16x  10
¯¯¯¯¯¯¯¯¯¯¯
m = 16
¯¯¯¯¯¯¯
b =  10
¯¯¯¯¯¯¯

From Keith Roberts: Hi Fapre,
Agree with Iobo that m is the slo...
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Wed, 09 May 2012 21:02:11 +0000
Hi Fapre,
Agree with Iobo that m is the slope of the tangent line and b is the yintercept of the tangent line. However, I would just add what the actual values are when applied to the parabola and its tangent you cited.
In this case, y' = 6x + 4 means that y'(2) = 16. So the the slope of the tangent line at x=2 is m=16.
To find b, the yintercept of the tangent line, just use y=mx+b, your point (2,22) as (x,y), and m=16:
That gives 22 = 16(2) + b, or b = 10. Thus the equation of the tangent line to the parabola is y = 16x  10.
To help reinforce your understanding of these concepts, I've searched and found a webpage and a video tutorial that address problems similar to this one, and I thought they might be helpful to you. I've listed them below.
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From frak1a12345: y = mx + b is known as the "slope/interce...
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Wed, 09 May 2012 20:55:15 +0000
y = mx + b is known as the "slope/intercept" form of a line equation.
m is the slope of the line and b is the y intercept of the line.
You plug in the 3 known quantities x, y and m (all are given to you) and solve for b.

From Anonymous: First, find the derivative:
dy/dx=6x+4
Now, ...
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Wed, 09 May 2012 20:51:55 +0000
First, find the derivative:
dy/dx=6x+4
Now, plug in x:
dy/dx=6(2)+4=16<this is your slope (m)
Now plug this into the y=mx+b equation given your x,y coordinates to solve for b:
22=16(2)+b
22=32+b
b=10
So:
m is 16
b is 10
And your equation is y=16x10

From lobo: m is slope of the tangent line
b is the y int...
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Wed, 09 May 2012 20:48:44 +0000
m is slope of the tangent line
b is the y intercept of the tangent line.