Question

True/False? The function f(x)=3cos(3x)-2sin(x) has at least one root in the interval [0,pi/2}.

Answer 1

Just do f(0) and f(pi/2)

Answer 2

if the signs are opposite then you win

Answer 3

first evaluate f(0) then f(pi/2)....so you get f(0)=3cos(0)-2sin(0)=3-0=3 and f(pi/2)=0-2=-2...so your function is continuous on the closed interval, so according to theorem it takes all the values between 0 and pi/2 so at some point it must have value zero, since it changes to negative to positive...

Answer 4

if I didn't mention true :D