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Question
Check whether the function f : R `rightarrow` R defined by f(x) = x3 + x, has any critical point/s or not ? If yes, then find the point/s.
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Solution
f(x) = x3 + x, for all x ∈ R.
`d/(dx) (f(x))` = f'(x) = 3x2 + 1; for all x ∈ R, x2 ≥ 0
`\implies` f'(x) > 0
Hence, no critical point exists.
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