Find the instantaneous rate of change of the function using definition.

Question

at 0

Answer 1

The instantaneous rate of change of f(x) at x is f'(x)

f'(x) = lim_(h→0) [(f(x+h) - f(x)) / h] = lim_(h→0) [(1/(x+h+1) - 1/(x+1)) / h] =

lim_(h→0) [(-h/((x+h+1)(x+1))) / h] = lim_(h→0) [-1 / ((x+h+1)(x+1))] = -1 / (x+1)²