Compute the first derivative like this:
[tex](6e^{rx})'=6re^{rx}[/tex]
Second derivative:
[tex](6re^{rx})'=6r^2e^{rx}[/tex]
From the given equation we get:
[tex]6r^2e^{rx}-6re^{rx}-42\times6e^{rx}=0[/tex]
Simplify like this:
[tex]6r^2-6r-252=0[/tex]
Solving the above equation for r we get:
r=-6 or r=7
