Question

How do you find the instantaneous rate of change for `f(x)= (x^2-2)/(x-1)` for x=2?

Answer 1

Differentiate using the quotient rule and then use the value of x to get `-2`

Explanation:

The rate of change is the derivative of the function. To find this we use the quotient rule `d/dx(f(x)/g(x)) =(g(x)f'(x) - g'(x)f(x))/(g(x)^2)`

`d/dx(f(x)/g(x)) = ((x-1)*2x - 1*(x^2 -2))/(x-1)^2`

`d/dx(f(x)/g(x)) = (2x^2 - 2x -x^2 +2)/(x-1)^2 = (x^2 - 2x - 2)/(x-1)^2`

If`x=2` the rate of change `(2^2 -2*2-2)/(2-1)^2 =-2/1 = -2`