Question

For the function \[ f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} - x^2 + x + 1, \] \( f'(1) = mf'(0) \), where \( m \) is equal to:

• A. 50
• B. 0
• C. 100
• D. 200

Hint:

Differentiate the function and evaluate at the required points to find the value of \( m \).

Answer 1

The Correct Option is C

Step 1: Differentiate the function.
First, differentiate the function \( f(x) \) with respect to \( x \), then evaluate the derivatives at \( x = 1 \) and \( x = 0 \). After calculations, we find that \( m = 100 \).
Thus, the correct answer is (3).