How do you determine all values of c that satisfy the mean value theorem on the interval [0,1] for # sqrt (x(1-x))#?
1 Answer
Jul 26, 2016
Explanation:
-
According to the therem,
#c# is all x-values that satisfy#f'(x)=(Deltaf(x))/(Deltax)# (within the given interval) -
#f(x)=sqrt(x(1−x))#
#f'(x)=( 1-2x)/(2sqrt(x(1−x)))# -
#(Deltaf(x))/(Deltax)=[f(1)-f(0)]/[1-0]=0# -
Equating,
#( 1-2x)/(2sqrt(x(1−x)))=0#
#1-2x=0#
#x=1/2#
#:.c=1/2#
