<p>You don’t need to do a sign chart if it’s asking for just a local minimum.</p>
<p>Find the derivative:</p>
<p>f’(x) = 3x^2 - 18x - 120</p>
<p>Set it equal to 0</p>
<p>x= 10 x = -4</p>
<p>Find the second derivative</p>
<p>f’’(x) = 6x - 18</p>
<p>Plug in the 10 and -4</p>
<p>f’’(10) = 42 It’s positive so it’s concave up</p>
<p>f’’(-4) = -42 It’s negative so it’s concave down</p>
<p>So the function has a local minimum at x=10</p>
<p>@izelkay you do understand that you are wasting your valuable seconds when you derive the function only to integrate it. If you integrate 2t-6 you get t^2-6t, aka the given function. All you have to do is x(4)-x(2). I don’t understand how you got 2 for your answer either.</p>
<p>Pretty sure you need to derive it to find out whether or not the particle changes directions.</p>
<p>so wait then when do you do a sign chart? I thought you always did for those kinds of problems…</p>
<p>Using a sign chart (though you can do it the other way):
f(x) = x^3 - 9x^2 -120x + 6
f’(x) = 3x^2 - 18x - 120
0 = 3x^2 - 18x - 120
x = 10 or x=-4</p>
<p>You take your x values and plug in numbers (into deriv) that are greater than and less than that x value. The sign of the value you get indicates an increasing or decreasing f. </p>
<h2>f’ (+) -4 (-) 10 (+)</h2>
<p>f inc. | dec. | inc.</p>
<pre><code> decreasing to increasing marks minimum
</code></pre>
<p>I hate related rates :(</p>
<p>Is there a good chance they will be on the free response?</p>
<p>Sent from my DROID Pro using CC</p>
<p>I guess you could, but finding the second derivative is easier and faster.</p>
<p>@Futurewolvering and Unseen:</p>
<p>My answer’s correct.</p>
<p>I googled it and it’s on here [Cracking</a> the AP Calculus AB & BC Exams - Princeton Review, David S. Kahn - Google Books](<a href=“Cracking the AP Calculus AB & BC Exams - David S. Kahn, Princeton Review (Firm) - Google Books”>Cracking the AP Calculus AB & BC Exams - David S. Kahn, Princeton Review (Firm) - Google Books) </p>
<p>page 114</p>
<p>I didn’t say 0 was the correct answer. Only that -8 - - 8 = 0.</p>
<p>ahhh ok thanks guys. the sign chart way is the only way I learned it in class so I don’t wanna confuse myself the night before</p>
<p>Oh my bad. Just Futurewolverine then. But yeah, you need to derive it to find out whether or not it changes directions.</p>
<p>@ mathisfun - There is a good chance there will be, unfortunately because i HATE them too!</p>
<p>didn’t study for it at all today #yolo</p>
<p>Here’s a Q: How do I know when I need to find the area between two curves with respect to y?</p>
<p>When you’re revolving around y-axis with disk/washer method, or</p>
<p>when you’re revolving around x-axis with shell method.</p>
<p>So if your just finding the area then it doesn’t matter whether dx or dy? Assuming everything is in the right terms.</p>
<p>Nope
10char</p>
<p>@unseen: Math is my weakest subject, so I’m sure there are more mathematical ways to say this. But when you integrate, you have two boundaries, “a” and “b”. Those boundaries are basically horizontal or vertical lines, either y=a or x=a respectively. Say, for example, you have two parallel lines with slope y=x that are bounded at the bottom by the x-axis and at the top by y=2. If you were to find the area with respect to x, you would have to make multiple integrals since the area’s boundaries are diagonals. On the other hand, you could find the area with respect to y and do one integral from a=0 to b=2 since they are bonded by horizontal lines at those points. It’s like tilting the way you look at the shape.</p>
<p>I don’t know if that makes sense, but you can do dx or dy. It’s just a matter of which ones faster. You can also use the disk/washer method with respect to y or x.</p>
<p>Thanks izelkay and injennious. I was looking through my notes and for some reason I had a page specifically for “Area with respect to y” and I got confused on whether it mattered. There goes fifteen minutes of study time.</p>
<p>[I</a> Will Derive! - YouTube](<a href=“I Will Derive! - YouTube”>I Will Derive! - YouTube)</p>
<p>So relevant… sooooo relevant…</p>