Find instantaneous rate of change of 7/3z^2

In summary, the instantaneous rate of change of 7/3z^2 is the derivative of the function at a specific point, and can be calculated using the formula f'(x) = lim(h → 0) (f(x+h) - f(x)) / h. It tells us the slope, direction, and steepness of the function at that point, and can vary at different points depending on the function's change. In real-world applications, it is useful for calculating velocities, accelerations, and rates of change in various systems, as well as analyzing trends and making predictions in economics and business.
  • #1
mattsoto
5
0
"Find the instantaneous rate of change of w with respect to z if w=(7/3z^2)"
excuse the primitive equation...any help?
 
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  • #2
Just http://mathworld.wolfram.com/Derivative.html" [Broken] it with respect to z.
 
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  • #3
Is that w= (7/3)z2 or w= 7/(3z2)?

I suspect the former which should be easy to differentiate using
(zn)'= n zn-1. If the latter, write it as w= (7/3)z-2 and use the same rule.
 

1. What is the instantaneous rate of change of 7/3z^2?

The instantaneous rate of change of 7/3z^2 refers to the rate at which the function changes at a specific point, or moment in time. It is also known as the derivative of the function at that point.

2. How is the instantaneous rate of change of 7/3z^2 calculated?

The instantaneous rate of change can be calculated using the formula: f'(x) = lim(h → 0) (f(x+h) - f(x)) / h. In the case of 7/3z^2, the derivative would be f'(z) = 14z/3.

3. What does the instantaneous rate of change tell us about the function?

The instantaneous rate of change tells us the slope of the function at a specific point. It can also be used to find the direction of the function's change and the steepness of the curve at that point.

4. How does the instantaneous rate of change vary at different points of the function?

The instantaneous rate of change can vary at different points of the function, as it is dependent on the slope of the function at that specific point. It can be positive, negative, or zero, depending on the direction of the function's change at that point.

5. How can the instantaneous rate of change be useful in real-world applications?

The instantaneous rate of change is useful in real-world applications, such as physics and engineering, to calculate velocities, accelerations, and rates of change in various systems. It can also be used in economics and business to analyze trends and make predictions about future changes.

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