Calculus:
How would I justify the relation of f(x), f'(x), and f"(x)? I'm having trouble explaining it.

Question

campbell_st · Answer

well given a function f(x) f'(x) is the instantaneous rate of change in the function at any point on the function. 

f''(x) is the instantaneous rate of change is f'(x) at any point on f(x)

anonymous · Answer

I don't quite understand what you mean? 
what I'm getting from what you are saying is that both f'(x) and f"(x) is the instantaneous rate of change? that can't be possible can it?

campbell_st · Answer

well if you have a function that shows distance travelled on time... the f(x) then f'(x) is the instantaneous rate of change in distance over time...(or velocity)

The rate of change in velocity over time is acceleration or f''(x)

dumbcow · Answer

f''(x) is the rate of the rate of change.

its like if you graphed f'(x), then the slope at any point would be f''(x)