Answer:
[tex]\frac{\frac{1000}{x+h}-\frac{1000}{x}}{h}[/tex] is your average rate of change,
Step-by-step explanation:
average rate of change is
[tex]\frac{f(a+h)-f(a)}{a+h-a}[/tex], by slope formula
simplify this to get [tex]\frac{f(a+h)-f(a)}{h}[/tex], which is the definition of the derivative as h goes to 0
[tex]\lim_{h \to 0} \frac{f(a+h)-f(a)}{h}[/tex]
since you defined x=a, we can substitute a for x and vice versa to find our derivative.
[tex]\lim_{h \to 0} \frac{(2x^2+\frac{1000}{x+h})-(2x^2+\frac{1000}{x})}{h}[/tex]
simplifying
[tex]\lim_{h \to 0} \frac{\frac{1000}{x+h}-\frac{1000}{x}}{h}[/tex] (your average rate of change)
