Question

When can instantaneous rate of change not be calculated?

Answer 1

The phrase "can [or cannot] be calculated" is ambiguous.

We can never finish with the decimal expansion for `sqrt2` or for `pi`, so should we say that they cannot be calculated?

There is no general method for solving polynomial equations of degree greater than 4 using algebraic expressions, but there are methods of successive approximation that will get us as close to the answer as you care to get.

The easy answer (for me) to this question is:

The instantaneous rate of change cannot be calculated when the limit:

`lim_(hrarr0) (f(x+h)-f(x))/h` cannot be calculated.

I'm not sure if that really answer the intended question.