1x3 find the difference quotient 1x3 find the difference quo

Solution

f(x) = 1/(x + 3)

f(x + h) = 1/(x + h + 3)

f(x + h) - f(x) = 1/(x + h + 3) - 1/(x + 3)

==> f(x + h) - f(x) = [(x + 3) - (x + h + 3)]/[(x + 3)(x + h + 3)]

==> f(x + h) - f(x) = -h/[(x + 3)(x + h + 3)]

==> [ f(x + h) - f(x) ]/h = -1/[(x + 3)(x + h + 3)]

difference quotient is [f(x + h) - f(x)]/h

==> Hence the difference quotient [f(x + h) - f(x)]/h = -1/[(x + 3)(x + h + 3)]