If d-d xFx-fx- then which of the following is-are antiderivative of fx -A- FxB- kF x - where k is a constantC- Fx-kD- Fx-k

The correct options are A F(x) C F(x) + k D F(x) kThe symbol ‘ ∫ ’ represents the anti derivative of a function. It means, by integrating f(x), we are trying ...

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Byju's Answer

Standard XII

Mathematics

Test for Monotonicity about a Point

If d/d xFx=fx...

Question

If $\frac{d}{d x}$ (F(x) ) = f(x), then which of the following is/are antiderivative of f(x) ?

F(x)

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kF(x), where k is a constant

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F(x) + k

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F(x) - k

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Solution

The correct options are
A F(x)
C F(x) + k
D F(x) - k
The symbol ‘ $\int$ ’ represents the anti derivative of a function. It means, by integrating f(x), we are trying to find a function, which when differentiated will give us f(x). We are given in question that derivative of F(x) is f(x). So, if we integrate f(x), we will get F(x). There is an important point to note here. We know that derivative of a constant is zero. So, the derivative of all the functions of the form F(x) + k, where k is a constant, will give f(x). So the answers are F(x), F(x)+k and F(x)-k

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If ddx (F(x) ) = f(x), then which of the following is/are antiderivative of f(x) ?

If $\frac{d}{d x}$ (F(x) ) = f(x), then which of the following is/are antiderivative of f(x) ?