DERIVATIVES:

For a function f(x), know that f(21)=79 and f'(21)= -5.
Estimate f(22), f(20), and f(24).

I don't won't you to do it for me but i need to know what formula to use.

Question

DERIVATIVES:

For a function  f(x), know that  f(21)=79 and  f'(21)= -5.
Estimate  f(22),  f(20), and  f(24).

I don't won't you to do it for me but i need to know what formula to use.

luffingsails · Answer

Remember what the first derivative indicates? It indicates the slope at a particular point in the function. So f'(21) = -5 means that the slope at x=21 is -5. That will give you an indication of behavior.

anonymous · Answer

@luffingsails 

For f(22) I did 79+(-5) = 74 so f(22) = 74
and for f(24) i did 79 + (-5(3))= 64 so f(24) = 64

For f(20) i'm confused on how to get my answer, instead of subtracting 5 do i add?

luffingsails · Answer

Not quite. Remember that the first derivative is the slope at that point. So instead of what you did... consider this graph:. Look at the slope at f(21) ant 

|dw:1427205931431:dw|

luffingsails · Answer

So, the function is decreasing as it goes right and increasing as it goes left. So, at x = 20, the function will have a value that is greater than 79 at x=21. Making sense?

anonymous · Answer

Yes

luffingsails · Answer

Okay, sorry if I wasn't clear at first. The answer really needed pictures.

anonymous · Answer

So f(20) is going to be bigger than f(21) How exactly would i get that answer?

anonymous · Answer

Actually nvm! i got it! Thanks for your help :D