To find the 4th derivative of h(x) = x² + 3x + 1, we first need to find the first, second and third derivatives:
First derivative:
h'(x) = 2x + 3
Second derivative:
h''(x) = 2
Third derivative:
h'''(x) = 0
Now, to find the fourth derivative, we simply take the derivative of h'''(x):
Fourth derivative:
h''''(x) = 0
Therefore, the fourth derivative of h(x) is 0.