derivitive of a function f at a number c
To find the derivative of a function f at a specific number c, we can use the definition of the derivative
To find the derivative of a function f at a specific number c, we can use the definition of the derivative.
The derivative of a function f(x) at a point c is defined as the limit of the difference quotient as x approaches c. This is expressed as:
f'(c) = lim (h -> 0) [f(c + h) – f(c)] / h
To calculate f'(c), we need to follow these steps:
Step 1: Substitute the value of x with c in the function f(x).
f(c) = f(c)
Step 2: Replace x with (c + h) in the function f(x).
f(c + h) = f(c + h)
Step 3: Calculate the difference between the two values obtained in Step 1 and Step 2.
[f(c + h) – f(c)] = f(c + h) – f(c)
Step 4: Divide the difference obtained in Step 3 by h.
[f(c + h) – f(c)] / h
Step 5: Taking the limit as h approaches 0 will give us the value of the derivative at c.
f'(c) = lim (h -> 0) [f(c + h) – f(c)] / h
It is important to note that the derivative of a function at a specific point represents the slope of the tangent line to the graph of the function at that point.
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