How do you find the absolute minimum and maximum on #[-pi/2,pi/2]# of the function #f(x)=sinx^2#?
1 Answer
Feb 20, 2015
Hello,
Answer. Minimum is 0 and maximum is 1.
-
If
#x# runs on#[-pi/2 , pi/2]# , then#x^2# runs on#[0,pi^2/4]# . So, you are looking for min and max of#sin# on the interval#[0,pi^2/4]# . -
Because
#pi/2 in [0,pi^2/4]# , the maximum is#1 = sin(pi/2)# . -
Because
#pi^2/4 < pi# , sin is positive on#[0,pi^2/4]# , so the minimum is#0= sin(0)# .
