Which one of the folloiwng is correct in respect of the function `f(x)=x(x-1)(x-1)` ?

Options

A. The local maximum value is larger than local minimum value
B. The local maxmum value is smaller than local minimum vlaue
C. The function has no local maximum
D. The function has no local minimum

Answer

B

Explanation

`f(x)=x(x-1)(x+1)=x(x^(2)-1)` m
Differentiating we get
`f'(x)=x(2)+(x^(2)-1)`
`f''(x)=6x`
`a f'(x)=0 rarr 3x^(2)-1 =0 rarr x^(2)=1/3 rarr x = pm (1)/sqrt(3)`
Maximum value of `f (x)=f((-1)/sqrt(3))=(-1)/sqrt(3)((-1)/sqrt(3))-1)`
`=(-1)/sqrt(3)(1/3-1)=(-1)/sqrt(3)((-2)/(3)=(2)/(3sqrt(3))`
Minimum value of f(x) `=((1)/sqrt(3))=(1)/sqrt(3)(1/3-1)=(-2)/(3sqrt(3))`