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Line Tangent ro a Parabolaby soul5
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#1
Mar2308, 05:16 PM

P: 64

1. The problem statement, all variables and given/known data
Find the point on the parabola y= 4x^2 + 2x  5 where the tangent line is perpendicular to the line 3x + 2y = 7. 2. Relevant equations 3. The attempt at a solution I don't know what to do since I was away the last 3 classes since I was away. Help me please. 


#2
Mar2308, 05:25 PM

P: 96

You want to find the slope of the line you're given and use the definition of a derivative as well as perpendicularity to solve for the x value you want.



#3
Mar2308, 05:27 PM

P: 459

Two perpendicular lines have slopes that are negative reciprocals of each other, eg: a line with a slope 2 is perpendicular to a line with a slope 1/2.
Find the slope of the line, find the negative reciprocal of that slope. The derivative of a function is the slope of that graph at any point on the graph, so find the derivative of the parabola and see at what value of x it will equal the negative reciprocal of the slope you found earlier. 


#4
Mar2308, 05:39 PM

P: 64

Line Tangent ro a Parabola
so..... 2y = 3x + 7 y= 3/2x + 7/2 slope = 3/2 so if it is perpendicular the slope is 2/3 is that my right slope? I now I have to do more but it that right so far? 


#5
Mar2308, 05:41 PM

P: 459

Yes.



#6
Mar2408, 01:51 PM

P: 63

Correct.
dy/dx = 8x+2 You want the value of x when dy/dx is (2/3), as you said from above. Solving for x gets (1/6). Plug this value into your original equation y=4x^2 etc. 


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