Consider the function f(x) = x(x - 1) (x - 2) ... (x - 100). Which one of the following is correct?

• A

  This function has 100 local maxima
• Correct answer
  B

  This function has 50 local maxima
• C

  This function has 51 local maxima
• D

  Local minima do not exist for this function

Solution

Hint : f(x) = x (x- 1) (x - 2) (x - 3) .... (x – 100)
by studying the graph we can see that f(x) is taking maximum value at 50 points

Hence, the correct answer is option: 'B'.