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**krutikahegde** Find a set of real numbers a, b, and c for which this piecewise-defined function is (everywhere) differentiable:

f(x)= tan^{-1}x, x≤ 0

f(x)= ax^{2} + bx + c, 0 < x < 2

f(x)= x^{3}- 1/4x^{2} + 5, x ≥ 2

so i plugged in x for the numbers and got:

tan^{-1}(0)= 0

a(0)^{2} + b(0) + c = 0

a(2)^{2} + b(2) + c= 4a+2b+0

(2)^{3}+ 1/4(2)^{2} + 5= 12

tan^{-1}(0)= a(0)^{2} + b(0) + c

c= 0

4a+2b= 12

-->2a+ b= 6

i didn't know how to do the rest from here.

please show all steps. thank you!