Find f(a), f(a + h),
and the difference quotient
f(a + h) − f(a)
------------------
h
,
where h ≠ 0.
f(x) = x/x+6
f(a)=
f(a + h) =
f(a + h) − f(a)
----------------- =
h
To find f(a), substitute the value of a into the expression for f(x):
f(a) = a / (a + 6)
To find f(a + h), substitute the value of a + h into the expression for f(x):
f(a + h) = (a + h) / (a + h + 6)
To find the difference quotient, subtract f(a) from f(a + h) and divide the result by h:
(f(a + h) - f(a)) / h = ((a + h) / (a + h + 6) - (a / (a + 6))) / h
Simplifying the difference quotient further involves combining the fractions and finding a common denominator.