Find f(a), f(a + h), and the difference quotient for the function given below, where h 0

Question

Find f(a), f(a + h), and the difference quotient for the function given below, where h  0

Answer 1

The difference quotient is defined as [ f(a+h) - f(a) ] / h .

Observe that f(a) = - 6/(a - 4) and f(a + h) = - 6 / [ (a+h) - 4 ] so that

[ f(a+h) - f(a) ] / h = {-6 / [ (a+h) - 4 ] + 6 /(a - 4) } / h = 6h / {(a-4)[(a+h) - 4]h} = 6 / {(a-4)[(a+h) - 4]}