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The maximum value of f(x)=(2x^2+2x+4)/(x...

The maximum value of `f(x)=(2x^2+2x+4)/(x^2+x+1) AA x in [0,1] is `

Text Solution

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`f(x) = (2x^2+2x+4)/(x^2+x+1)`
`=>f(x) = (2(x^2+x+2))/(x^2+x+1)`
`=>f(x) = (2(x^2+x+1+1))/(x^2+x+1)`
`=>f(x) = 2(1+1/(x^2+x+1))`
Now, `f(x)` will be maximum when `x^2+x+1` is minimum.
Now, we will try to draw the graph for `x^2+x+1.`
Please refer to video to see the grah.
From the graph, we can see that minimum value of `x^2+x+1` is `1` as `x in [0,1]`.
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