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

f(x)

=*cx*^{2} + 8*x* if
*x* < 3

=*x*^{3}? *cx*
if *x* ?
3

## Answer

*cx*^{2} + 8*x* =
*x*^{3} ? *cx*

put x=3

9c+24 = 27 - 3c

c=1/4

**f(3-) = c*3 ^{2} + 8*3 = 9c+24**

**f(3+)= 3 ^{3}-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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