Test a rule against a difference quotient

You will write three functions that test the product rule and the quotient rule by computer. A function and its derivative are passed in as Python functions. The checker uses $u = x^2$ with $v = \sin x$, and $u = x^2 + 1$ with $v = x - 1$.

The idea. The product rule gives $u'v + uv'$ and the quotient rule gives $\dfrac{u'v - uv'}{v^2}$. A rule is right if its value agrees with the central difference quotient $\dfrac{f(x + h) - f(x - h)}{2h}$ for a small $h$.

Your tasks.

1. Finish product_rule(u, du, v, dv, x). Return the value of $u'v + uv'$ at x.
2. Finish quotient_rule(u, du, v, dv, x). Return the value of $\dfrac{u'v - uv'}{v^2}$ at x.
3. Finish agrees(f, rule_value, x). Return True when rule_value is within 0.0001 of the central difference quotient of f at x, with h = 0.00001.