Struggling on this question, how would I solve this in the most simple way possible?

Question

(No calculator allowed)

Find all of the critical numbers for f(x) = 3sinx - 3xcosx.

A) x = 2kpi for any integer k

B) x = (2k + 1)pi for any integer k

C) x = (2k+1)pi/2 for any integer k

D) x = kpi for any integer k

Edit: I got option D, but I'm not sure if it's correct. Could someone confirm?

Edit 2: Nevermind, I got it correct!

Answer 1

Answer 2

f(x) = 3sinx - 3xcosx

f'(x) = 3cosx -3(cosx - xsinx) = 3xsinx

Critical points when f'(x) = 0.

3xsinx = 0

x = 0 or sinx = 0

sinx = 0 when x = 0, ±π, ±2π, ±3π, ...

So, x = kπ, where k is any integer.