For what value of the constant c is the function f continuous on (−∞ ∞)

For what value of the constant c is the function f continuous on (-infinity, infinity)?

f(x)

=cx2 + 8x    if x < 3

=x3? cx if x ? 3

Answer

cx2 + 8x   = x3 ? cx

put x=3

9c+24 = 27 - 3c

c=1/4

f(3-) = c*32 + 8*3 = 9c+24

f(3+)= 33-3c = 27-3c

to make the function countinous f(3-) = f(3+)

9c+24 =27-3c

12c= 3

c= 1/4

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