f ‘(x) is the limit of the following difference quotient as x approaches c
To find the limit of the difference quotient as x approaches c, we need to start with the definition of the derivative of a function
To find the limit of the difference quotient as x approaches c, we need to start with the definition of the derivative of a function.
The derivative of a function f(x) at a point c, denoted as f'(c), is defined as:
f'(c) = lim(h→0) ((f(c + h) – f(c)) / h)
In this case, we are given f'(x) instead of f(c). So, we need to find the limit of the difference quotient as x approaches c. Let’s denote c as the given value for x.
f ‘(x) = lim(h→0) ((f(x + h) – f(x)) / h)
This expression represents the derivative of f(x) evaluated at any x-value, x = c.
To find the value of f ‘(x) at a specific value of x, substitute the value of x into the above expression and evaluate the limit as h approaches 0.
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