How to Find Tangent Lines to Y=x^2 Passing Through (2,3) [SOLVED] Tangent Line

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Homework Help Overview

The problem involves finding all tangent lines to the curve defined by the equation Y=x^2 that pass through the point (2,3). The subject area is calculus, specifically focusing on derivatives and tangent lines.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to find the correct point on the curve where the tangent line touches, as well as the corresponding slope derived from the derivative of the function. There is uncertainty about how to determine this point.

Discussion Status

The discussion includes attempts to clarify the relationship between the slope of the tangent line and the point of tangency on the curve. Some participants provide guidance on deriving the line equation once the slope is known, while others express confusion about identifying the appropriate point on the curve.

Contextual Notes

Participants highlight the challenge of not having the specific point of tangency, which is necessary to calculate the slope accurately. There is an emphasis on understanding the setup of the problem before proceeding with the solution.

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[SOLVED] Tangent Line

Homework Statement


Find all tangent lines that are tangent to Y=x^2 and go through the point (2,3)


Homework Equations





The Attempt at a Solution



At first I thought I knew how to do this problem, I found the derivative of the equation got:

y' = 2x ; then I plugged in x=2 to find the slope of the tangent however then i realized this is not the correct point to plug in because this is not the point that the line is actually going to be hitting the original graph at; I don't know how you would find this said point to plug in for x to get the slope can anyone steer me in the right direction
 
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You are looking for a line. You have the slope, and a point that the line goes through. That's sufficient information to derive the line equation.
 
I don't have the slope though because I don't know what point the line is tangent to on the curve so how can i plug a value into the derivative to get slope
 
y' = 2x is the family of all lines that are tangent to x^2. You are supposed to find the one that goes through (2,3).
 
oh i see thank you for your help :)
 

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