Mark M. answered • 11/10/17

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f(x) = 3 √x - sinx (note that x ≥ 0)

f'(0) = lim

_{h→0}[ (f(0+h) - f(0))/h ] = lim

_{h→0 }[ (3√h - sinh) / h ] = lim

_{h→0}[3/√h - sinh/h] = ∞ - 1 = ∞The given function is NOT differentiable when x = 0. The function has a vertical tangent at the point (0,0).

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