Find the absolute maximum value and the absolute minimum value of `f(x)=2x^3-15x^2+36x+1` in `[1, 5]`

Explanation

Given : `f(x)=2 x^{3}-15 x^{2}+36 x+1`

`Rightarrow f^{prime}(x)=6 x^{2}-30 x+36`

For a local maximum or a local minimum

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

`Rightarrow 6 x^{2}-30 x+36=0 `

`Rightarrow x^{2}-5 x+6=0 `

`Rightarrow(x-3)(x-2)=0`

`Rightarrow x=2 and x=3`

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