<p>Well then I’m confused, now for a polynomial function if
f’'(c) = 0, then at c is there ALWAYS an inflection point? I want to say yes, but now I am not sure. But as I said before if there is an inflection point at x = 1, then on the interval (0, 2) there IS a change in concavity, because 1 lies on the interval (0, 2), thats what an inflection point is, the exact point where a change in concavity takes place I want to say D & E. I am going to ask my teacher tomorrow about it.</p>
<p>Do you know when you will get the answer for this question?</p>
<p>Possibly monday or tuesday. I have to hand in the HW tomorrow or monday if my teachers absent (Snow storm in NY)</p>
<p>Btw, if I remember correctly, for point of inflection, don’t you have to prove that a number less than the point of inflection and a number greater than the point is different in signs?</p>
<p>Lets say its this
f(0)=5
f(1)=0
f(1.3) = .8
f(1.7) = 0
f(2)=-7</p>
<p>The signs wouldn’t have changed then.</p>
<p>I’ll post what my teacher says about it, please post what the answer is when you get it.</p>
<p>Edited my previous response, maybe that might help pick a answer</p>
<p>the philanthropy on these threads always warms my heart :D</p>
<p>Yes! I am pretty sure you are right, I was trying to think why x = 1 wouldn’t necessarily be an inflection point and you gave me the answer. The chart doesnt tell us whether f’’ is positive or negative at values very close to x=1, meaning it doesn’t say whether f’‘(.99) is positive or whether f’‘(1.01) is negative. Therefore, I do not think there is sufficient evidence to say that f’'(1) is an inflection point, but it does change concavity on the interval (0, 2). (I picked .99 and 1.01 arbitrarily btw)</p>
<p>Well I talked to my teacher about the problem and he agreed with what I initially stated, that the answer is both D & E, for the reasons I have already said. Please let me know when you get it graded or whatever because I am interested in what the correct answer is.</p>
<p>lim sinx/x approaching 0, =1 . Genius.</p>
<p>jerry’s is the best way for people not in diffyque</p>
<p>Significa’s explanation is correct on the point of inflection question. In order to have a point of inflection, the only requirement is that you show that f "(x) changes signs. We frequently look for where f "(x) = 0 to find where these sign changes happen, but f "(x) = 0 is not enough by itself to guarantee that an inflection point has occurred. Significa’s chart helps to illustrate a possible way that an inflection point might not occur at x = 1.</p>
<p>Got the answer today, it was indeed E. Thanks for the help guys =]</p>
<p>If you’re solving the differential equation, you’re looking for the anti-derivative right?
ex. solve the following differential equation: dy/dx = 4^x - sinx</p>
<p>dy = (4^x - sin)dx</p>
<p>∫1dy = ∫(4^x - sin)dx</p>
<p>y = (4^x)/(log[4]) - cos + C</p>