NDA2018MathematicsDifferentiationActual
If f(x) is an even function, where f(x) 0 , then which one of the following is correct?
Options
- Af ^ ( x ) is an even function
- Bf^ (x) is an odd function
- Cf^ (x) may be an even or odd function depending on the type of function
- Df ^ ( x ) is a constant function
Correct answer
B. f^ (x) is an odd function
Step-by-step solution
f ( x ) is an even function. Let's see some examples (1) If f(x)= x , which is even function, f^ ( x )=- x , which is odd function. (2) If f(x)=x^2 , which is even function, f^ ( x )=2 x , which is odd function.