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Last edited by learningtoneopet1; 11-22-2013 at 12:01 AM.
Not on these specific types of problems I'm working on It's where you are given one of the following: The graph of f(x), the graph of f'(x), or the graph of f''(x). They don't give you any function whatsoever, and you just have to use the graph they give you to estimate what the other two look like. I know how to do it when I start with the f(x) graph, but if I'm given the other ones, I have no clue cause there's a few rules which dictate how you should draw the graph, which I don't know.
These are the rules that I found on a website which would help in sketching the functions, but I really don't know how to do that.... For example, if you had the graph of the function f''(x) = 2, you would have to analyze it using those rules to go backwards and find out that f'(x) = 2x and f(x) = x^2
1. If the first derivative f' is positive (+) , then the function f is increasing ($ \uparrow $) .
2. If the first derivative f' is negative (-) , then the function f is decreasing ( $ \downarrow $) .
3. If the second derivative f'' is positive (+) , then the function f is concave up ($ \cup $) .
4. If the second derivative f'' is negative (-) , then the function f is concave down ($ \cap $) .
5. The point x=a determines a relative maximum for function f if f is continuous at x=a , and the first derivative f' is positive (+) for x<a and negative (-) for x>a . The point x=a determines an absolute maximum for function f if it corresponds to the largest y-value in the range of f .
6. The point x=a determines a relative minimum for function f if f is continuous at x=a , and the first derivative f' is negative (-) for x<a and positive (+) for x>a . The point x=a determines an absolute minimum for function f if it corresponds to the smallest y-value in the range of f .
7. The point x=a determines an inflection point for function f if f is continuous at x=a , and the second derivative f'' is negative (-) for x<a and positive (+) for x>a , or if f'' is positive (+) for x<a and negative (-) for x>a .
---------- Post added at 11:30 PM ---------- Previous post was at 11:28 PM ----------
Thanks! And the 30 min mark isn't the limit, just would prefer to have it done by then can really push it off for another 30 mins max
Edit: If I need to explain anything about what I have to do in more detail, feel free to tell my anyone I'm not super good at explaining
Last edited by learningtoneopet1; 11-21-2013 at 11:33 PM.
Your multi-step process makes me think that you need to plot it on a line graph to help determine the direction?
Do you do a table for your 2X and X^2 stuff?
---------- Post added at 11:59 PM ---------- Previous post was at 11:58 PM ----------
Oh and I realize I'm grasping at straws. Really wish I recalled this stuff.
if anyone needs any more calculus/math/physics help, pm me guys
learningtoneopet1(11-22-2013),Skarl (11-22-2013)