Answer:
c= -1.8
Step-by-step explanation:
A function is continuous at a point x if the limits at x from above and below coincide (are equal). Hence,
Limit from above: [tex]\lim_{x\rightarrow\-1^+}f(x)=4c(-1)=6 = -4c-6[/tex]
Limit from below: [tex]\lim_{x\rightarrow\-1^-}f(x)=c(-1)^2+3=c+3[/tex]
And so when these limits are equal we obtain
[tex]c+3=-4c-6\\5c=-9\\c=-1.8[/tex]
