Question

Determine the values of the constants B and C so that the function given below is differentiable.
f(x){ 11x x<=1
{ Bx^2+Cx 1

Answer 1

A function is differentiable if f(a)^- = f(a) = f(a)^+
f(1) = 11(1) = Bx^2 + Cx = B(1)^2 + C(1) = B + C
B + C = 11 . . . (1)
Also, f'(1) = 11 = 2Bx + C = 2B(1) + C = 2B + C
2B + C = 11 . . . (2)

(2) - (1) => B = 0
C = 11