Just took the test on Curve Sketching and Interpreting Derivatives and now I’m mad and upset, so please excuse me if it sounds like I’m ranting.
Why is it so easy to so many other people but ridiculously difficult to me? I can’t see the relationships between f, f’, f’’, and f’’’ on the graph alone. I HAVE to draw the derivative charts to see the relationships! What do the zeros of the f’ graph mean to the f graph? Or to the f’’ graph? I don’t know!
And even if I do do it this way, the test took way too long for me to finish. There was no way I could even BS the questions since I HAD to show work to get any credit! There’s no way I’m getting a B in that test. I feel like punching a wall.
Okay, I’m done ranting. I don’t take failure very well, as you saw. I just don’t have that interpretive sense that others in my Calculus class have, and my GPA is going to suffer because of it. And there are no opportunities for re-tests.
Someone please help. Where do I go from here? The class is not going to slow down. I want to understand it but I can’t. And I’m still in the middle of college apps. What should I do from here?
Yes, but I still don’t get it. I have a tutor who comes by my place by appointment, but I still didn’t get it. I looked it up on Khan Academy but it still wasn’t clear.
It’s been 20 years since I taught calc, so bear with me:
You wrote: " I can’t see the relationships between f, f’, f’’, and f’’’ on the graph alone. I HAVE to draw the derivative charts to see the relationships! What do the zeros of the f’ graph mean to the f graph? Or to the f’’ graph? I don’t know!"
It sounds to me as though you’re lacking in a basic understanding of what those things mean.
f’(x) is the derivative, the slope of the tangent to the curve at that point. So if the tangent is positive, the slope is positive-- the curve is increasing. If the slope of the tangent is negative, the curve is going down, so the curve is decreasing.
When the slope of the tangent (still the derivative, f’(x) ) is zero, it’s either a max, a min, or a point of inflection.
Now let’s look at f’'(x)-- and check me here, my memory is rusty.
I think that when f’‘(x) is positive, it’s a min-- is that right? And f’'(x) is neg when it’s a max?
OK, bigger issue: it sounds like you need to start attending extra help. Get there early next week, so you can find time over Thanksgiving weekend to pull your notes together. It may help if you can borrow someone else’s notes-- that kid who is nice and always pulls the nice grades? Go through his/her notes and I bet you see lots of little reminders-- notes she has written to herself to explain stuff. (When I’m teaching, I use pink on the Ipad for that stuff; it really stands out!)
Google teacher websites until you find a calc teacher somewhere in this country with a great website, full of videos and explanations. Or try teachertube.com – kind of like youtube, but just teacher made videos. You may find something there to help.