Finding the gradient of a chord

In summary, the conversation is discussing the gradient of the chord of the curve y = 2x^2 between the points x = 1 and x = 1+ h. The homework equations being used are differentiation by first principles and dy/dx = f(x+h) - f(x)/h. The solution is 4x + 2h, and it is suggested to sketch the graph to understand why the solution should be in terms of h alone. The conversation also mentions that the gradient of a line does not depend on x.
  • #1
einstein101
9
0

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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  • #2
Cool! Erm... what was your question?
Shouldn't your solution be in terms of h alone?
 
  • #3
Why h alone, is it because i have to sub x for 1 ?
 
  • #4
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?
 

What is the gradient of a chord?

The gradient of a chord is the measure of the slope or steepness of a line segment that connects two points on a curve.

How do you find the gradient of a chord?

To find the gradient of a chord, you need to first determine the coordinates of the two points on the curve that the chord connects. Then, you can use the formula (y2 - y1) / (x2 - x1) to calculate the gradient.

Is the gradient of a chord the same as the gradient of a curve?

No, the gradient of a chord is only a measure of the slope between two points on a curve, while the gradient of a curve is a measure of the slope at a specific point on the curve. The gradient of a curve can change depending on the point chosen, while the gradient of a chord remains constant.

Can the gradient of a chord be negative?

Yes, the gradient of a chord can be positive, negative, or zero. A positive gradient indicates an upward slope, a negative gradient indicates a downward slope, and a zero gradient indicates a horizontal line.

Why is finding the gradient of a chord important?

Finding the gradient of a chord is important in mathematics and science because it allows us to calculate the rate of change between two points on a curve. This is useful in various fields, such as physics, engineering, and economics.

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