Question

Let \( f(x) = 25x^{24}(1 - x)^{75} \), on the interval \( [0, 1] \), then \[ f'(x) = 25x^{24}(1 - x)^{75} - 75x^{25}(1 - x)^{74} = 25x^{24}(1 - x)^{74}[(1 - x) - 3x] \]

• A. \( \frac{1}{4} \)
• B. \( \frac{1}{2} \)
• C. \( 1 \)
• D. \( 0 \)

Hint:

To find the maximum or minimum of a function, compute its derivative and solve for critical points.

Answer 1

The Correct Option is A

After simplifying the derivative, we find that the maximum of \( f(x) \) occurs at \( x = \frac{1}{4} \).