Question

For the function f(x)=4/x+3 average rate of change of f from 1 to x. How to even start with this?

Answer 1

Average rate of change of function from a to b is: { f(b) - f(a) } / (b - a)

Average rate of change of function from 1 to x is: { f(x) - f(1) } / (x - 1)

Find f(1) and substitute into the above formula and simplify.

Answer 2

So f(1)= 4/ (1) +3
4/4=1?

Answer 3

Yes. Also substitute f(x) = 4 / (x+3) in the formula and simplify.

Answer 4

Example? 4/ (x+3) x+3?

Answer 5

Average rate of change of function from 1 to x is: { f(x) - f(1) } / (x - 1)
f(x) = 4 / (x+3)
f(1) = 4 / (1+3) = 4/4 = 1

{ f(x) - f(1) } / (x - 1) = { 4 / (x+3) - 1 } / (x - 1) =
{ 4 - x - 3 } / { (x+3)(x-1) } = (1-x) / { (x+3)(x-1) } =
- (x-1) / { (x+3)(x-1) } = -1 / (x+3)

Answer 6

Thanks!

Answer 7

You are welcome.