# Finding the instantaneous velocity of a scalar function?

• supermiedos
In summary, the problem given by the professor of finding the instantaneous velocity of f(x, y, z) = xyz at (1, 2, 1) seems to be incorrectly formulated. The only time instantaneous velocity was calculated was when dealing with a vectorial function. Attempts to use dw were unsuccessful due to a lack of information on dx, dy, and dz. There is no additional information provided.
supermiedos

## Homework Statement

Find the instantaneous velocity of f(x, y, z) = xyz, at (1, 2, 1)

## The Attempt at a Solution

I think this problem our proffesor gave us wasn't formulated correctly. The only time when we calculated instantaneous velocity was when we had a vectorial function like r(t) = x(t) i + y(t) j + z(t) k.

I tried using dw, but it doesn't work since i don't know dx, dy or dz

supermiedos said:

## Homework Statement

Find the instantaneous velocity of f(x, y, z) = xyz, at (1, 2, 1)

## The Attempt at a Solution

I think this problem our proffesor gave us wasn't formulated correctly. The only time when we calculated instantaneous velocity was when we had a vectorial function like r(t) = x(t) i + y(t) j + z(t) k.

I tried using dw, but it doesn't work since i don't know dx, dy or dz

No, I don't think the phrasing of the question makes much sense.

Just to make sure, is there any information that you omitted, like values for dx/dt, dy/dt, and dz/dt? If not, then I concur with Dick.

I knew it! No, there's no more information. Only f and the point (1, 2, 1). Thanks!

## 1. What is instantaneous velocity?

Instantaneous velocity is the rate of change in an object's position at a specific moment in time. It is the velocity of an object at a single point rather than over a period of time.

## 2. How is instantaneous velocity different from average velocity?

Average velocity is the total displacement of an object over a period of time, while instantaneous velocity is the velocity at a specific moment in time. Average velocity can be calculated by dividing the total displacement by the total time, while instantaneous velocity can be found by taking the derivative of the position function with respect to time.

## 3. What is a scalar function?

A scalar function is a mathematical function that takes in one or more variables and outputs a single scalar value. In the context of finding instantaneous velocity, the scalar function would be the equation representing the object's position as a function of time.

## 4. How do you find the instantaneous velocity of a scalar function?

To find the instantaneous velocity of a scalar function, you must take the derivative of the function with respect to time. This will give you the velocity of the object at a specific moment in time.

## 5. Why is finding the instantaneous velocity important?

Finding the instantaneous velocity of an object is important because it allows us to understand the object's motion at a specific point in time. This information is crucial in many scientific fields, such as physics and engineering, as it helps us analyze and predict the behavior of objects in motion.

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