When does f'(x) = f(x)?
- Tim Brzezinski
Is there a certain base value of a for which f'(x) = f(x) for all x? If so, what do you think this particular base value is?
Use the formal limit definition of a derivative to show that if , then , where k is a scalar.
For the previous question, what is the exact value of this constant (scalar) k?
Use your results from the previous two questions to formally prove that f'(x) = f(x) for all x in the domain of f when k = the value you provided in response to question (1).