Question 462141
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The average rate of change is simply the slope of the secant line through the two points (x,f(x)) and (x+h,f(x+h)), so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{f(x\,+\,h)\ -\ f(x)}{h}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ 6\ -\ x^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x\ +\ h)\ =\ 6\ -\ (x^2\ +\ 2xh\ +\ h^2) =\ 6\ -\ x^2\ -\ 2xh\ -\ h^2]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{6\ -\ x^2\ -\ 2xh\ -\ h^2\ -\ (6\ -\ x^2)}{h}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{6\ -\ x^2\ -\ 2xh\ -\ h^2\ -\ 6\ +\ x^2}{h}\ =\ -2x\ -\ h]




John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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