## SanjanaP 7 months ago Help with Increasing and Decreasing Derivatives Please!!

1. myininaya

what is the question exactly?

2. myininaya

If f'>0, then f is increasing If f'<0, then f is decreasing

3. SanjanaP

Oh...sorry I thought I had the attachment on

4. SanjanaP

I neeed help with C and D

5. SanjanaP

@myininaya

6. myininaya

so are you having problems with the part highlighted in yellow?

7. SanjanaP

Basically...

8. myininaya

ok then so you know that g' will tell us if g is decreasing or increasing right?

9. SanjanaP

Yeah

10. myininaya

so find g' given that: $g(x)=\int\limits_{0}^{x} f(t) dt$ don't look at the picture yet just tell what g' is

11. SanjanaP

f(x)+0.5

12. SanjanaP

F(x)+c right?

13. myininaya

no i'm sorry that isn't correct ok let's look at this... I will rewrite it a little... $g(x)=F(x)-F(0)$ where F'=f Now differentiate to find g'

14. SanjanaP

I'm sorry..so what is g'?

15. myininaya

you have to differentiate g(x)=F(x)-F(0) to find g' can you do that?

16. SanjanaP

I'm not sure what differentiate means anymore?

17. myininaya

to find derivative

18. SanjanaP

It's f'(x)-f'(0)

19. SanjanaP

f'(x)(x) right?

20. myininaya

I will help you out some more. derivative of g is g' derivative of F is f (this was given above when I said F'=f) derivative of a constant is 0 everything i said in this little post right here will need to be used

21. SanjanaP

oh....so the derivative of F(x) is f(x). Is that what you mean?

22. myininaya

That is what I said

23. myininaya

so do you know F(0) is a constant?

24. SanjanaP

its 0.5

25. myininaya

I think you are thinking of f(0) not F(0) f is given not F

26. SanjanaP

yea?

27. myininaya

Anyways F(0) is a constant. Because F is a just a function of x any if you plug in a number for x then you will definitely receive a constant ---------------------------------------------------- example: Say F(x)=cos(x) well F(0) is definitely a constant because F(0) is 1 and 1 never changes (it is and will always remain 1)

28. myininaya

So going back to $g(x)=\int\limits_{0}^{x} f(t) dt \\ g(x)=F(x)-F(0)$ can you differentiate g now?

29. myininaya

what that means is you will have to differentiate both sides (not just one side)

30. SanjanaP

Can you just tell me where it is increasing and concave up...so I'll try to figure it out?

31. myininaya

Try to use what I said earlier... derivative of g is g' derivative of F' is f derivative of a constant is 0 you can do this

32. SanjanaP

I would prefer the answer because I have to write the explanation anyway.

33. SanjanaP

Okay...so you g(x)= F(x)-F(0)

34. SanjanaP

that means g'(x) = f(x)-0?

35. myininaya

I'm not going to give just the answer. Sorry. But right g'=f so that means the picture given is g'

36. myininaya

and you know if g'>0, then g is increasing and you know if g'<0, then g is decreasing

37. myininaya

where on the picture that is given is g' above the x axis (because that is where g is increasing) and when g' is below the x-axis that is where g is decreasing

38. SanjanaP