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Find the maximum and minimum values of t...

Find the maximum and minimum values of the function `y=x^(3) , "in" x in [-2,3]`?

Text Solution

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`(dy)/(dx)=3x^(2)`
`(dy)/(dx)=0 at x=0 `(Point of inflection )
`(dy)/(dx) ge 0 "for" AA x in R `
So, function is strictly increasing .
For a monotonic function maximum and minimum value always occur at end points .
So, `y_("max")=27`
`y_("min")=-8`
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