Let , where are real valued functions of . Statement I is not differentiable at 3…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let h(x)=f1(x)+f2(x)+f3(x)+⋯+fn(x)h(x) = f_1(x) + f_2(x) + f_3(x) + \dots + f_n(x) , where f1(x),f2(x),f3(x),…,fn(x)f_1(x), f_2(x), f_3(x), \dots, f_n(x) are real valued functions of xx . Statement I f(x)=∣cos⁡∣x∣∣+cos⁡−1(sgn x)+∣ln⁡∣x∣∣f(x) = |\cos |x|| + \cos^{-1}(\text{sgn } x) + |\ln |x|| is not differentiable at 3 points in (0,2π)(0, 2\pi) . Statement II Exactly one function, is fi(x)f_i(x) , i=1,2,…,ni = 1, 2, \dots, n is not differentiable and the rest of the function is differentiable at x=ax = a makes h(x)h(x) not differentiable at x=ax = a .

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