Question

Determine the second derivative evaluated at t=0

Answer 1

If

`M(t) = e^(3(e^t-1))`

then using the chain rule, we have

`M'(t) = e^(3(e^t-1)) * 3e^t = 3e^(3(e^t-1)+t)`

`M''(t) = 3e^(3(e^t-1)+t) * (3e^t+1)`

Then

`M''(0) = 3e^(3(e^0-1)+0) * (3e^0+1) = 3e^0 * (3+1) = \boxed{12}`