Question

Help on a Cal1 lab question. w/photo.

Answer 1

Would I take the derivative of h with respect to V? Then explain it like that?

Answer 2

Steepness is a measurement of the slope, in this case the slope\[m =\frac{ \Delta h }{ \Delta V }\]Indirectly, this states that the steepness (the slope) inversely varies with the change in the volume. This implies that as the change in volume increases, the slope decreases. Conversely, as the change in the volume decreases, the slope increases. Good Luck!!

Answer 3

The derivative is the slope of any tangent to a curve.

Answer 4

Thus the derivative here would imply\[\lim_{\Delta V \rightarrow 0}\frac{\Delta h }{ \Delta V}\]

Answer 5

Would it make sense to say if the amount of change height increases for successive amounts of changes of volume, the rate of change of the function is increasing on the interval?

Answer 6

Sorry, had to step away for a few minutes plus lost the internet connection for a second. Your explanation doesn't answer or demonstrate full comprehension of the problem.

Answer 7

I pretty much gave you a complete generalization. Now simply apply that knowledge to the problem. In other words, read the question, look at the diagram, and my notes above should make sense.

Answer 8

haha. No problem. Yeah, I got it now. Thanks!