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

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Chapter 2, 2.1 - Problem 16 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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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

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