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 ----------
Yeah I don't remember any of that. Sorry. :( I hope ya find help though! I kinda remember enjoying calculus.
Thanks! And the 30 min mark isn't the limit, just would prefer to have it done by then :P 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 :P I'm not super good at explaining