Linear approximation and error

You will write three functions: the linear estimate of $f(x)$ from a nearby point $a$, the percentage error of an estimate, and a helper that finds the perfect square nearest to a number. The checker tests several functions.

The idea. The estimate is $f(x) \approx f(a) + f'(a)(x - a)$. The derivative $f'(a)$ can be found from a short balanced interval. The percentage error is $\dfrac{|\text{true} - \text{estimate}|}{|\text{true}|} \times 100$.

Your tasks.

1. Finish linear_estimate(f, a, x).
2. Finish percent_error(true, estimate).
3. Finish nearest_square(n). Return the perfect square closest to n, as a whole number.