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Note that f is continuous on (−∞, 6) and (6, ∞). For the function to be continuous on (−∞, ∞), we need to ensure that as x approaches 6, the left and right limits match.

First we find the left limit.
lim
x→6−
f(x) =
lim
x→6−
(cx2 + 3x)

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1 answer

  1. evidently
    f(x) = 6 - c x^2 - 3 x
    left of x = 6

    but you do not say what your function is to the right of 6

    anyway the idea is to find c so that the functions are the same at x = 6

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