Question 2.10.4: Finding Every Function with a Given Derivative Find all func...
Finding Every Function with a Given Derivative
Find all functions that have a derivative equal to 3 x^2+1.
We first write down (from our experience with derivatives) one function
with the correct derivative: x^3+x. Then, Corollary 10.1 tells us that any other function with the same derivative differs by at most a constant. So, every function whose derivative equals 3 x² + 1 has the form x^3+x+c , for some constant c.
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