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Mathematics
Which one of the following statements is NOT CORRECT ?
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Q. Which one of the following statements is NOT CORRECT ?
Continuity and Differentiability
A
The derivative of a diffrentiable periodic function is a periodic function with the same period.
B
If $f ( x )$ and $g ( x )$ both are defined on the entire number line and are aperiodic then the function $F(x)=f(x) \cdot g(x)$ can not be periodic.
C
Derivative of an even differentiable function is an odd function and derivative of an odd differentiable function is an even function.
D
Every function $f ( x )$ can be represented as the sum of an even and an odd function
Solution:
For $(B)$ : consider $f(x)=x-\sqrt{x^2+1}$ and $g(x)=x+\sqrt{x^2+1}$ then $F(x)=1$ which is periodic $\Rightarrow$ False