Finding the gradient of a chord

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Homework Help Overview

The discussion revolves around finding the gradient of a chord of the curve defined by the equation y = 2x², specifically between the points x = 1 and x = 1 + h. The problem involves concepts from calculus, particularly differentiation and the interpretation of gradients.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply differentiation by first principles to find the gradient, while some participants question the need for the solution to be expressed solely in terms of h. Others suggest that sketching the graph may clarify the relationship between the points and the gradient.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem. There is a focus on understanding the implications of using h in the solution and whether the gradient depends on x. Guidance has been offered regarding the graphical representation of the problem.

Contextual Notes

Participants are considering the implications of substituting specific values for x and the assumptions related to the gradient of a line connecting two points on the curve.

einstein101
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Homework Statement



What is the gradient of the chord of the curve y = 2x^2 between the points x = 1 and x = 1+ h?

Homework Equations


differentiation by first principles

dy/dx = f(x+h) - f(x)/h

The Attempt at a Solution



use of the formula to receive 4x +2h
 
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Cool! Erm... what was your question?
Shouldn't your solution be in terms of h alone?
 
Why h alone, is it because i have to sub x for 1 ?
 
Sketch the graph and you'll see for yourself:

You are drawing a line through points (1,2) and (h,2h2) and finding the gradient of that line. Does the gradient of a line depend on x at all?
 

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