Question

Please help?

the graphs of f, f', and f" and are shown on the same set of coordinate axes. Which is which? Explain your reasoning.

Answer 1

i think the curve is f, f' is the slanted line and f" is the horizontal. am i right?

Answer 2

f is of degree 2, f' is of degree 1 and f'' is a constant.
I think that you are correct.
No substitute for having the actual expression for f.

Answer 3

@VIbarguen1 You're right. Why?

Well you should check to make sure, since the derivative is just the slope formula, only marginally more fancy, you can make a pretty good estimate.

For instance, what you're calling f is the curve, so as you follow along from left to right, you can see that it's sloping down, sloping less down, sloping even less down until it doesn't slope at all, then slopes up, up more, even more, etc... and so now you can see that literally corresponds to negative, less negative, zero, positive, more positive, right? That sounds like that slanted line passing straight through the origin. The other line doesn't even touch zero!

Now what about the slanted line, how's the slope change as you move from left to right? It has the same slope everywhere, so that's just that constant line. So hopefully this reinforces your reasoning and makes it start to make even more sense.

Answer 4

yeah it does. thank you very much

Answer 5

Cool, if you have any other questions about calculus feel free to ask. =)