How do you determine all values of c that satisfy the mean value theorem on the interval [0,1] for # sqrt (x(1x))#?
1 Answer
Jul 26, 2016
Explanation:

According to the therem,
#c# is all xvalues that satisfy#f'(x)=(Deltaf(x))/(Deltax)# (within the given interval) 
#f(x)=sqrt(x(1−x))#
#f'(x)=( 12x)/(2sqrt(x(1−x)))# 
#(Deltaf(x))/(Deltax)=[f(1)f(0)]/[10]=0# 
Equating,
#( 12x)/(2sqrt(x(1−x)))=0#
#12x=0#
#x=1/2#
#:.c=1/2#