If , where 's are real constants, then…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

If f(x)=∑i=1nai∣x∣f(x) = \sum_{i=1}^{n} a_i |x| , where aia_i 's are real constants, then f(x)f(x) is (1) continuous at x=0x = 0 for all aia_i (2) differentiable at x=0x = 0 for all ai∈Ra_i \in R (3) differentiable at x=0x = 0 , for all a2k+1=0a_{2k+1} = 0 (4) None of the above

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