# Maximum gradient of a normal to the curve

• abdo799
In summary, the conversation discusses a homework problem involving finding the point where the gradient of the normal is maximum. The solution involves finding the stationary points of the family of tangent lines and using the definition of gradient. Algebra and understanding of the concepts involved are necessary for solving the problem.
abdo799

## Homework Statement

complete problem attached

## The Attempt at a Solution

part I in this question was a bit tricky but i managed to solve it , when i read part II i understood nothing , he usually asks about the tangent not the normal , he asks about the point where the gradient of the normal is maximum and i have no idea how to get this , when i read the answers he said we should differentiate again then = it to 0 to find x , why did this work?

#### Attachments

• 2014-03-29 12_25_25-papers.xtremepapers.com_CIE_Cambridge International A and AS Level_Mathemati.png
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The tangent lines intersecting the given equation form a family, one for each point. Right?
The normal line is simply obtained from any straight line, right?
That makes the set of normals a family of lines intersecting the given eqn at every point on it.
From there, it is a simple application of the definition of gradient. Oh, and obviously of finding the stationary points of that family. Not sure what else to tell you. It seems to be straighforward algebra as long as you understand what the various things are you are dealing with (and can differentiate simple functions).

i got it...thanks

## 1. What is the maximum gradient of a normal to the curve?

The maximum gradient of a normal to the curve is the steepest slope perpendicular to the curve at a specific point.

## 2. How is the maximum gradient of a normal to the curve calculated?

The maximum gradient of a normal to the curve is calculated by finding the derivative of the curve at a specific point and then finding the slope of the line perpendicular to the derivative at that point.

## 3. What does the maximum gradient of a normal to the curve represent?

The maximum gradient of a normal to the curve represents the rate of change of the curve at a specific point, and the direction in which the curve is changing at that point.

## 4. Can the maximum gradient of a normal to the curve be negative?

Yes, the maximum gradient of a normal to the curve can be negative. This indicates that the curve is decreasing in the direction perpendicular to that point.

## 5. How is the maximum gradient of a normal to the curve useful in real-world applications?

The maximum gradient of a normal to the curve is useful in real-world applications such as physics, engineering, and economics, where it can help determine the optimal path or direction for a given situation. It is also used in computer graphics to create realistic 3D images.

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