Find values of the constants $k$ and $m$, if possible, that will make the function continuous everywhere.

Question

Find values of the constants $k$ and $m$, if possible, that will make the funtion continuous everywhere. $$ f(x) = \begin{cases} x^2+5, & x > 2, \\ m(x+1)+k, & -1 < x \leq 2, \\ 2x^3+x+7, & x \leq -1. \end{cases} $$

Answer 1

Hint: you want

$$\lim_{x \to 2^+ }(x^2+5)=\lim_{x \to 2^{-}}(m(x+1)+k)$$ $$\lim_{x \to -1^+ }(m(x+1)+k)=\lim_{x \to -1^{-}}(2x^3+x+7)$$