Mathematics

Mathematics

Problem

In which one of the following functions, Rolle's theorem is applicable? (a) f(x)=∣x∣f(x) = |x|, in −2≤x≤2-2 \leq x \leq 2 (b) f(x)=tan⁡xf(x) = \tan x, in 0≤x≤π0 \leq x \leq \pi (c) f(x)=1+(x−2)2/3f(x) = 1 + (x-2)^{2/3}, in 1≤x≤31 \leq x \leq 3 (d) f(x)=x(x−2)2f(x) = x(x-2)^2 in 0≤x≤20 \leq x \leq 2 (a) f(x)=∣x∣f(x) = |x|, in −2≤x≤2-2 \leq x \leq 2 (b) f(x)=tan⁡xf(x) = \tan x, in 0≤x≤π0 \leq x \leq \pi (c) f(x)=1+(x−2)2/3f(x) = 1 + (x-2)^{2/3}, in 1≤x≤31 \leq x \leq 3 (d) f(x)=x(x−2)2f(x) = x(x-2)^2 in 0≤x≤20 \leq x \leq 2

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