2. Consider a function g defined piecewise as follows, where c is an (as-yet ) undetermined constant: x2 - 5x+3 ifx 0, the derivative is given by g'(x) = 4x + c. Consequently, lim g'(x) = -2(0) -5 = -5 and lim g'(x) = 4(0) + c = c x-+0 x->0+ Therefore, if we choose c = -5, then g is differentiable at x = 0, and g' (0) = -5