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Question
Discuss extreme values of the function f(x) = x.logx
Solution
f(x) = x.logx
Differentiating w.r.t. x,
`f'(x) = x . 1/x + logx.1`
f'(x) = 1 + logx
Differentiating again w.r.t. x,
`f''(x) = 1/x`
For maxima or minima,
f'(x) = 0
∴ 1 + logx = 0
∴ logx = -1
∴ x = `e^-1`
∴ `f''(1/e) = 1/(1/e)`
∴ `f''(1/e) = e`
∴ `f''(1/e) > 0`
∴ f(x) is minimum at x = `1/e`
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