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

c=1/2

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