How do you determine all values of c that satisfy the mean value theorem on the interval [0,1] for sqrt (x(1-x))√x(1−x)?
1 Answer
Jul 26, 2016
Explanation:
-
According to the therem,
cc is all x-values that satisfyf'(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