Question

If \( f(x) = -2x^8 \), then the correct statement is :

• A. \( f'( \frac{1}{2} ) = f( - \frac{1}{2} ) \)
• B. \( f'( \frac{1}{2} ) = - f( - \frac{1}{2} ) \)
• C. \( -f( \frac{1}{2} ) = f( - \frac{1}{2} ) \)
• D. \( f'( \frac{1}{2} ) = - f( \frac{1}{2} ) \)

Hint:

Odd functions satisfy the property \( f(-x) = -f(x) \).

Answer 1

The Correct Option is B

The function is odd because it is an even-powered term. For odd functions, \( f(-x) = -f(x) \). Therefore, the correct answer is that \( f'( \frac{1}{2} ) = - f( - \frac{1}{2} ) \).