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

solution:

f(x) has discontinuity at x=3

if it is continuous at x=3

then the continuous on (-\infty ,\infty )

we have,

f(x)= \left \{cx^{2}+8 ; if x< 3,x^{3}-cx ;if x\geq3

\lim_{x\rightarrow 3^-}f(x)=\lim_{x\rightarrow3^+}f(x)

\lim_{x\rightarrow3^-}(x^{2}+8x)=\lim_{x\rightarrow3^+}(x^{3}-cx)

(9c+24)= (227-3c)

9c+24=27-3c

9c+3c=27-24

12c=3

c=\frac{1}{4}

i believe it's a.

i'm not sure on this one, most likely correct.

-1/3(x+1)^5

i’m pretty sure this is correct