Question

Create a function that has a derivative of f(x) = 2x + 1 at a given input value of your choice.

Answer 1

The opposite operation to taking a derivative is an integral. Integrate to find original function.

f(x) = x^2 + x + C

C is constant because we didn't have bounds on the integral. it lets you choose the input value let's say is just (1,0)

0 = 1 + 1 + C
- 2 = C

function at input value (1,0)
f(x) = x^2 + x - 2

now if you check by taking derivative is :
f' = 2x + 1