Which Equation Has the Greatest Rate of Change?

In summary, the conversation discusses the concept of derivative and its relation to the rate of change. The equation with the greatest rate of change is determined by the value of the first derivative, which can be either a scalar or a vector. However, in this case, both equations have the same rate of change as the derivative is a scalar value.
  • #1
GreenPrint
1,196
0

Homework Statement



I believe it is no?
I'm asked which equation has the greatest rate of change, first derivative, going back to the deffinition of derivative I would say yes...

Well there are two equations I calculated the first derivative in one to be 2 and the other one to be -2... so if the derivative is a vector which my gut tells me it is then 2 would be the correct answer becasue it's greater in value than -2 but if the derivative is a scalar and only has direction the both answers have the greatest...

I also have a hunch that technically speaking right the derivative has no width right and so therefore is neither a scalar or a vector so...

please help which one has the greatest rate of change the one with the first derivative of 2 or -2... I don't know if it's a vector or not...

THANK YOU!

Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
  • #2
Given an equation dependent on only one variable (say x), the derivative evaluated at a point for that equation is a scalar value, not a vector.

The rate of change they are asking for seems to be "direction" independent and so in your case the two functions have equal rates of change.
 

1. What is a derivative as a vector?

A derivative as a vector is a mathematical concept that represents the rate of change of a function at a specific point. It is a vector because it has both magnitude and direction, with the magnitude being the slope of the function and the direction pointing in the direction of the increase of the function.

2. How is a derivative as a vector different from a regular derivative?

A regular derivative is a scalar quantity that represents the instantaneous rate of change of a function at a specific point. A derivative as a vector, on the other hand, not only tells us the rate of change but also the direction of the change.

3. What is the geometric interpretation of a derivative as a vector?

The geometric interpretation of a derivative as a vector is that it represents the tangent line to the function at a specific point. The direction of the vector is the same as the direction of the tangent line, and the magnitude is equal to the slope of the tangent line.

4. How is a derivative as a vector used in physics?

In physics, a derivative as a vector is used to describe the velocity and acceleration of an object. The velocity of an object is the derivative of its position with respect to time, and the acceleration is the derivative of its velocity with respect to time. These derivatives are vectors because they have both magnitude and direction.

5. Can a derivative as a vector be negative?

Yes, a derivative as a vector can be negative. This indicates that the function is decreasing in value at that point. The negative sign in the vector represents the direction of the decrease.

Similar threads

Lagrange multipliers understanding
    • Calculus and Beyond Homework Help
Replies
8
Views
470
Multivariable calculus problem involving partial derivatives along a surface
    • Calculus and Beyond Homework Help
Replies
9
Views
714
Correct Usage of Partial Derivative Symbols in PDEs
    • Calculus and Beyond Homework Help
Replies
10
Views
912
Given unit impulse response, obtain differential equation
    • Calculus and Beyond Homework Help
Replies
7
Views
284
Instantaneous rate of change and deriving a fraction
    • Calculus and Beyond Homework Help
Replies
23
Views
2K
A different related rates problem - no time mentioned
    • Calculus and Beyond Homework Help
Replies
13
Views
1K
Related rates: How fast is a runner going to 1st base, as seen from 2nd base?
    • Calculus and Beyond Homework Help
Replies
6
Views
608
Finding the derivative and rate of change
    • Calculus and Beyond Homework Help
Replies
7
Views
1K
Frequencies for harmonic oscillator with multiple periodic solutions?
    • Calculus and Beyond Homework Help
Replies
6
Views
239
How to approach vector calculus identities?
    • Calculus and Beyond Homework Help
Replies
9
Views
1K

Hot Threads

Recent Insights

Back
Top