Given that the function $ f\left(x\right) = \left\{ \begin{array}{lr} ax+2 & 0 \le x \le 1\\ bx^2 +3ax +5 & 1<x \le 2\\ e^{2x} +b & 2 < x \le 3\\ (cx+3)^2 +2ax & 3 < x \le 4\\ \end{array} \right.\\$
is continuous on the interval $[0,4]$. Find the values of $a,b $ and $ c$
I tried solving by equating right side limit of $1$ to the left side limit ($ax +2$ and $bx^2 + 3ax + 5$) but got stuck with equations.
Guide:
At $x=1$, you get $a(1)+2=b(1)^2+3a(1)+5$.
Similarly, you should be able to get equations at $x=2$ and $x=3$ respectively.
Now, solve the linear system of equations.