Question

Let f(x) = x sin πx, x > 0. Then for all natural numbers n, f'(x) vanishes at

(A) a unique point in the interval (n,n + 1/2)

(B) a unique point in the interval (n + 1/2 , n + 1)

(C) a unique point in the interval (n, n + 1)

(D) two points in the interval (n, n + 1)

Answer 1

(B) a unique point in the interval (n + 1/2 , n + 1)

(C) a unique point in the interval (n, n + 1)

We have f'(x) = sinπx + πx cosπx = 0

⇒ tanπx = -πx