Tangent/Normal with derivative

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Homework Help Overview

The problem involves finding the tangent and normal lines to the curve y=x³ at the point (1,1), focusing on the derivatives and slopes of these lines.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the slopes of the tangent and normal lines by calculating the derivative and substituting the point of interest. Some participants affirm the calculations without raising further questions.

Discussion Status

The discussion appears to be supportive, with participants confirming the original poster's findings regarding the slopes of the tangent and normal lines. There is no indication of unresolved issues or alternative interpretations being explored.

Contextual Notes

There is a mention of uncertainty regarding the correctness of the slope calculations, but this has not led to further inquiry or clarification from other participants.

iRaid
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Homework Statement


Find the lines that are (a) tangent and (b) normal to the curve y=x3 at the point (1,1).

Homework Equations


The Attempt at a Solution


So first I found the derivative, 3x2. Then I used x=1 to find the slope which is 3.

(a)y-1=3(x-1)
y=3x-2

(b)y-1=(-1/3)(x-1)
y=(-1/3)x+(4/3)Not really sure if I found the slope correctly tho..
 
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It looks good to me.

If two lines are perpendicular, then the product of their slopes is -1 .
 
Looks good to me. I see no problem with a or b.
 
Thanks :p
 

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