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Question
If f(x) = `1/(4x^2 + 2x + 1)`, then its maximum value is ______.
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Solution
If f(x) = `1/(4x^2 + 2x + 1)`, then its maximum value is `4/3`.
Explanation:
For f to be maximum, 4x2 + 2x + 1 should be minimum
i.e. 4x2 + 2x + 1 = `4(x + 1/4)^2 + (1 - 1/4)` giving the minimum value of 4x2 + 2x + 1 = `3/4`.
Hence maximum value of f = `4/3`.
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