Question

If f' = f and f(0) = 0, find f(b) for b = 1, 2, 3, 4, 5, 6?

Answer 1

The function f(x) = 0 for all values of x.

Step-by-step explanation:

To find f(b) for the given function f'(x) = f(x) and f(0) = 0, we need to use the concept of exponential functions. The solution to this differential equation is f(x) = Cex where C is a constant. Since f(0) = 0, we can substitute this into the equation to find C = 0. Therefore, the function becomes f(x) = 0. Now we can find f(b) for each value of b given: f(1) = 0, f(2) = 0, f(3) = 0, f(4) = 0, f(5) = 0, f(6) = 0.