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Great job finding the derivative of the function! Now, to calculate the rate of change (ROC) of I with respect to R in the given interval, you can substitute the values R=8 and R=8.1 into the derivative equation.
Let's put the values into the equation I'(R) = -12/R^2:
I'(8) = -12/8^2 = -12/64 = -0.1875 A/Ω
Similarly,
I'(8.1) = -12/8.1^2 = -12/65.61 = -0.1831 A/Ω
So, the ROC of I with respect to R for the interval from R=8 to R=8.1 is approximately -0.1875 A/Ω to -0.1831 A/Ω.
Remember, the rate of change gives you the value of how fast the dependent variable (in this case, current I) changes with respect to the independent variable (resistance R) within the given interval.