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Let f(x) = x1/2(x - 2), x ∈ R & x > 0. Then the critical point of f is |
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Answer» f(x)= \(x^\frac12\)(x - 2), x ∈ R & x > 0 . Domain of f(x) is (0 , 0). ∴ f1(x) = \(x^\frac12\) + \(\frac12\)\(x^\frac{-1}2\)(x - 2) for critical point, we have f1(x) = 0 ∴ \(x^\frac12\) + \(\frac12\)\(x^\frac{-1}2\)(x - 2) = 0 \(\Rightarrow\) 2x + x - 2 = 0 ( on multiplying both sides by \(2x^\frac{1}2\)) \(\Rightarrow\) 3x - 2 = 0 \(\Rightarrow\) x = \(\frac23\) Hence, x = \(\frac23\) is a critical point of f. |
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