A continuous and differentiable function will have a un
A. True
B. False
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
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 ddx(F(x)) = f(x).
We saw that in that case, ∫f(x)=F(x)+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.