`f(x) = 5 - (2/3) x` Find the derivative of the function by the limit process.

Expert Answers
hkj1385 eNotes educator| Certified Educator

By limit process, the derivative of a function f(x) is :-

f'(x) = lim h --> 0 [{f(x+h) - f(x)}/h]

Now, the given function is :-

f(x) = 5 - (3/2)x

Thus, f'(x) = lim t --> 0 [{f(x+t) - f(x)}/t]

or, f'(x) = lim t ---> 0 [{{5 - (2/3)*(x+t)} - {5 - (2/3)x}}/t] 

or, f'(x) = lim t ---> 0 [{-(2/3)t}/t] = -2/3