a unique point in the interval (n, n+1)
a unique point in the interval (n+1/2, n+1)
two points in the interval (n, n+1)
a unique point in the interval (n, n+1/2)
The correct options are
B a unique point in the interval (n+1/2, n+1)
C a unique point in the interval (n, n+1)
Given that f(x) = xsin(πx) ⇒ f'(x) = sin(πx) + πxcos(πx)
f'(x) = 0 ⇒ sin(πx) + πxcos(πx) = 0
⇒ tan(πx) = -πx
⇒ πx ∈ ((2n+1)π/2, (n+1)π) ⇒ x ∈ (n+1/2, n+1) and also x ∈ (n, n+1).