Answer
$y'' = 12\theta + 14$
$y'''= 12$
Work Step by Step
First, we can distribute the $\theta^2$ to simplify the problem:
$y = 2\theta^3 + 7\theta^2$
To find the second derivative, you need to find the first derivative first, so we differentiate the equation using the power rule:
$y' = 6\theta^2 + 14\theta$
Then we find the derivative of $y'$ to find $y''$ using the power rule:
$y'' = 12\theta + 14$
Finally, to find $y'''$, we find the derivative of $y''$ as follows:
$y'''= 12$
