Question

A continuous and differentiable function will have a unique derivative and a unique anti derivative

• A. True
• B. False

Answer 1

The correct option is B False

We have to check if the derivative and anti derivative of a function are unique. By unique, we mean, when we differentiate a function, we should get only one function. Similarly when we integrate a function, we should get only one function.
Let $\frac{d}{dx}$(F(x)) = f(x).
We saw that in that case, $\int f\left(x\right)=F\left(x\right)+C$, where c is any number.
We know that the functions F(x) and F(x)+5 are different. So, as we change c, we get different functions. This means, when we integrate a function, we get a collection of functions, which differ by a constant. We will say the integral or antiderivative does not give a unique function, even though derivative of a function is unique. So the given statement is wrong.