(Solved): Determine if the piecewise-defined function is differentiable at the origin. f(x)= 4x + tanx, x20 3 ...

Determine if the piecewise-defined function is differentiable at the origin. f(x)= 4x + tanx, x20 3x² x<0 Select the correct choice below and, if necessary, fill in the answer boxes in your choice. OA. The function is not differentiable at the origin because lim f(0+h)-f(0) and limi h h-0 A-0 (Type integers or simplified fractions.) OB. The function is differentiable at the origin because it is continuous at x = 0 and lim f(0+h)-f(0) h h?0 (Type integers or simplified fractions.) C. The function is not differentiable at the origin because it is not continuous at x = 0. f(0+h)-f(0) h and lim h?0.* f(0+h)-f(0) h