Can instantaneous rate of change be negative?

Answer 1
Most certainly! When the instantaneous rate of change of a function at a given point is negative, it simply means that the function is decreasing at that point. As an example, given a function of the form #y=mx+b#, when m is positive, the function is increasing, but when m is negative, the function is decreasing. For a line, the rate of change at any given point is simply m.

This is also evident in physics: if your acceleration, or rate of change of velocity, is positive, you are moving in a "positive" direction (e.g., towards the right on a number line); if it is negative, you are moving in a "negative" direction (e.g., towards the left on the number line). Additionally, if your acceleration, or rate of change of velocity, is positive, you are increasing; if it is negative, you are decreasing.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Yes, the instantaneous rate of change can be negative. This occurs when the function is decreasing at a particular point, meaning that the slope of the tangent line to the curve at that point is negative.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7