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Lagrange's theorem applicable for \( f(x)=x^{4 / 3} \) in \( [-1,1] \) |
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Answer» f(x) = x4/3, x ∈ [-1, 1] \(\because\) f(x) is continuous when x ∈[-1, 1]. and f-1(x) = d/dx(x4/3) = 4/3 x4/3 - 1 = 4/3 x1/3 \(\therefore\) f-1(x) is continuous when x ∈ [-1, 1]. \(\because\) Given function is satisfies both required conditions of Lagrange theorem. \(\therefore\) Lagrange theorem is applicable for f(x) = x4/3 in x ∈ [-1, 1]. |
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