Let f(x)={(1+x)23,−2≤x<0(3x−5)2,0≤x≤2f(x) = \begin{cases} (1+x)^{\frac{2}{3}}, & -2 \leq x < 0 \\ (3x-5)^2, & 0 \leq x \leq 2 \end{cases}…

Mathematics

Problem

Let f(x)={(1+x)23,−2≤x<0(3x−5)2,0≤x≤2f(x) = \begin{cases} (1+x)^{\frac{2}{3}}, & -2 \leq x < 0 \\ (3x-5)^2, & 0 \leq x \leq 2 \end{cases} Which one of the following statements is correct? (a) f(x)f(x) is continuous at each point on [−2,2][-2, 2] (b) f(x)f(x) is differentiable for all xx in (−2,2)(-2, 2). (c) Rolle's Theorem is applicable for f(x)f(x) in [−2,2][-2, 2]. (d) There exists at least one c∈(−2,2)c \in (-2, 2) for which f′(c)=0f'(c) = 0 (a) f(x)f(x) is continuous at each point on [−2,2][-2, 2] (b) f(x)f(x) is differentiable for all xx in (−2,2)(-2, 2). (c) Rolle's Theorem is applicable for f(x)f(x) in [−2,2][-2, 2]. (d) There exists at least one c∈(−2,2)c \in (-2, 2) for which f′(c)=0f'(c) = 0

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