Please HELP with this problem?

Question

For the function y = f(x), what does the quotient, f(b) – f(a) / b – a as b approaches a, represent?

a) The instantaneous rate of change for f(x) at a
b) The average rate of change for f(x) over the interval a is less-than-or-equal-to x which is less-than-or-equal-to b
c) The mean value of f(x)
d) The instantaneous rate of change for f(x) over the interval a is less-than-or-equal-to x which is less-than-or-equal-to b

Answer 1

The limit of this as b tends to a is the instantaneous rate of change at x=a, ie f'(a), so its answer a) from the list

Answer 2

a) The instantaneous rate of change for f(x) at a
This is the definition of the derivative of the function at a, which, if it exists, will give you the slope of a line tangent to the function at a.

Answer 3

a