Which Equation Has the Greatest Rate of Change?

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SUMMARY

The discussion centers on determining which of two equations has the greatest rate of change based on their first derivatives. One equation has a first derivative of 2, while the other has a first derivative of -2. The consensus is that the derivative, evaluated at a point for a single-variable equation, is a scalar value, not a vector. Therefore, both equations exhibit equal rates of change when considering the absolute value of their derivatives.

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  • Familiarity with the definition of rate of change
  • Knowledge of scalar versus vector quantities
  • Ability to evaluate first derivatives of functions
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  • Learn about the concept of absolute value in relation to rates of change
  • Explore the differences between scalar and vector quantities in mathematics
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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!

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The Attempt at a Solution

 
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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.
 

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