Question

If f(x)=2x^2+(1000/x), find the average rate of change of f(x) from x=a to x=a+h.

Answer 1

Answer:

$\frac{\frac{1000}{x+h}-\frac{1000}{x}}{h}$ is your average rate of change,

Step-by-step explanation:

average rate of change is

$\frac{f(a+h)-f(a)}{a+h-a}$, by slope formula

simplify this to get $\frac{f(a+h)-f(a)}{h}$, which is the definition of the derivative as h goes to 0

$\lim_{h \to 0} \frac{f(a+h)-f(a)}{h}$

since you defined x=a, we can substitute a for x and vice versa to find our derivative.

$\lim_{h \to 0} \frac{(2x^2+\frac{1000}{x+h})-(2x^2+\frac{1000}{x})}{h}$

simplifying

$\lim_{h \to 0} \frac{\frac{1000}{x+h}-\frac{1000}{x}}{h}$ (your average rate of change)