Find f(a), f(a + h),
and the difference quotient
f(a + h) − f(a)
------------------
h
,
where h ≠ 0.
f(x) = 2x/x-7
f(a)=
f(a + h) =
f(a + h) − f(a)
----------------- =
h
To find f(a), we substitute the value a into the function f(x) = 2x/(x-7):
f(a) = 2a/(a-7)
To find f(a + h), we substitute (a + h) into the function f(x):
f(a + h) = 2(a + h)/((a + h) - 7)
To find the difference quotient (f(a + h) - f(a))/h, we subtract f(a) from f(a + h) and divide by h:
(f(a+h) - f(a))/h = (2(a + h)/((a + h) - 7) - 2a/(a - 7))/h
Simplifying the expression further is difficult without specific numerical values for a and h.