Find the maximum value of `2x^3-24 x+107` in the interval `[1,\ 3]` . Find the maximum value of the same function in `[-3,\ -1]` .

Explanation

`f(x)=2 x^{3}-24 x+107`

`Rightarrow f^{prime}(x)=6 x^{2}-24=6(x^{2}-4)=6(x+2)(x-2)`

Critical points

`f^{prime}(x)=0 Rightarrow 6(x+2)(x-2)=0 Rightarrow x=2,-2`

(i) first the interval `[1,3]`.

`x=2` in this interval

`x=1, quad f(1)=2 times 1^{3}-24 times 1+107=85`

`x=2, quad f(2)=2 times 2^{3}-24 times 2+107=75`

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