Find the absolute maximum and the absolute minimum values of the following function in the given intervals: `f(x)=(x-2)sqrt(x-1)" in "[1,9]`

Explanation

`f(x)=(x-2) sqrt{x-1}` in `[1,9]`

`f^{prime}(x)=sqrt{x-1}+frac{(x-2)}{2 sqrt{x-1}}`

critical points `f^{prime}(x)=0`

`Rightarrow sqrt{x-1}+frac{(x-2)}{2 sqrt{x-1}}=0`

`Rightarrow frac{2(x-1)+(x-2)}{2 sqrt{x-1}}=0`

`Rightarrow frac{3 x-4}{2 sqrt{x-1}}=0`

`Rightarrow x=frac{4}{3}`

`f(1)=0`

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