Equations and Tangents for Curve C at Point P

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Homework Help Overview

The discussion revolves around finding equations related to a curve C, specifically at a point P (1,4). The gradient of the curve is provided as dy/dx = (3x-1)², and participants are tasked with deriving the normal line at point P, the equation of the curve, and analyzing the tangent's behavior in relation to a given line.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the process of finding the normal line and express confusion regarding the requirements of part b), particularly the integration of the derivative to find the original function. There is also a focus on verifying results through differentiation.

Discussion Status

Some participants have provided guidance on the integration process needed for part b) and emphasized the importance of checking answers through differentiation. Multiple interpretations of the problem are being explored, particularly regarding the integration and the implications of the wording in the question.

Contextual Notes

There is an indication that participants are working under homework constraints, which may limit the information they can use or reference. The need to clarify assumptions and the specific requirements of each part of the problem is evident.

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The gradient of the curve C is given by: dy/dx = (3x-1)2
the point P (1,4) lies on C.

a) Find an equation of the normal to C at P.
b) Find an equation for the curve C in the form y=f(x)
c) using dy/dx = (3x-1)2 show that there is no point on C at which the tangent is parallel to the line y=1-2x.

Well for a) i got: 4y= -x+17 (subbed x= 1 in dy/dx, got grad of normal and got eq)

But, i don't understand what part b) wants me to do. I think i could do c) by using the gradients and showing that they're not the same.

Some help on b) please!
 
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You have the derivative of the function y=f(x). Do you know how to get the original function back from its derivative? Do you know why they said to "find an equation" instead of "find the equation" in b)?
 
do you mean i have to integrate dy/dx = (3x-1)2 for b)

to get : 3x3 - 3x2+x +c ?
 
Last edited:
Integration is the correct operation. But your answer is not correct yet. You should be able to check your answer by differentiating it again to get back to the original equation for dy/dx.
 
oh wait i remembered i need work out c, by using P(1,4)

Thanks for your help!
 
Your welcome. Be sure to do the step where you check your answer using differentiation.
 

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