Question

For what value of the constant c is the function f continuous on the interval negative infinity to positive infinity?

f(x)={cx2+7x if x<2
x3−cx if x> or =2

Answer 1

look at the "transition point"

in f(x) = cx^2 + 7x
f(2) = 4c + 14

in f(x) = x^3 - cx
f(2) = 8 - 2c

to be continuous the y values must be the same
4c + 14 = 8 - 2c
6c = -6
c = -1

Answer 2

thank you! I actually figuredit out right after I submitted this lol