The value of c in (0,2) satisfying the Mean Value theorem for the function `f(x)=x(x-1)^(2), x epsilon[0,2]` is equal to

Options

A. `3/4`
B. `4/3`
C. `1/3`
D. `2/3`

Answer

B

Explanation

given `f(x)=x(x-1)^(2)`
`impliesf'(x)=2x(x-1)+(x-1)^(2)`
`=(x-1)(2x+x-1)=(x-1)(3x-1)`
Now `f'(c)=(f(2)-f(0))/(2-0)`
`implies(c-1s)(3c-1)=(2-0)/2=1`
`implies3c^(2)-4c=0`
`impliesc(3c-4)=0`
`impliesc=0` of `c=4/3`
`:.` The value of c in (0,2) is `4/3`