<p>HA! i can't resist :D</p>
<p>h''(x) = -4cos(2x) + 2sin(x)</p>
<p>graphical analysis...mehhhh. :(</p>
<p>As i have given up all hope of an acceptance, I have reverted back to my studies. Currently, I am studying for the calc bc ap, and I am having trouble with the following question. Please help!</p>
<p>Find the second derivative, and conduct a graphical analysis of the following function: </p>
<p>h(x) = cos(2x) - 2sin(x)</p>
<p>*Note: you will need to remember your identities as well as the the quad. form to solve this...</p>
<p>Please help - this will surely pass some of the wait time!</p>
<p>-PS</p>
<p>hm. idk how that randomly got out of order.</p>
<p>I'm not sure what you mean by graphical analysis, but isn't it just:</p>
<p>h(x) = cos(2x) - 2sin(x)</p>
<p>h'(x) = -2sin(2x) - 2cos(x)</p>
<p>h"(x) = -4cos(2x) + 2sin(x)</p>
<p>Max is right on with the second derivative.
Just find critical numbers and points of inflection. I would do it, but quad. formula = suck.</p>
<p>For CN, set first derivative = to 0
For POI, set second derivative = to 0</p>
<p>Then do the first and second derivative tests.</p>
<p>Or just graph it on a calculator.</p>
<p>Thank you for your answers, HOWEVER, I realize that i have mistyped my question, what the book is asking for is the SIMPLIFIED DOUBLE DERIVATIVE, so that I can obtain the ZERO VALUES without using a calculator. </p>
<p>I have already done the simplified version of f prime: below
h prime (x) = -2cos(x) [ 2sin(x) + 1]</p>
<p>But what i still need is the simplified version of f double prime: PLEASE HELP!</p>
<p>and this is aperson who wants to go to stanford?.....</p>
<p>phi6 - I appreciate your derogatory tone, you obviously paid a lot of attention to my initial post when I said I was "reviewing" (as in past material), and "forgot" how to obtain the second derivative to a simplified form. Judging by the fact that no one has answered my question fully, and has only provided me with a preliminary non-simplified (though correct) second derivative, my question is obviously not that simple. </p>
<p>Once again, no need to be condescending, I was merely asking a review question, and I don't think it merited such a remark. Good luck everyone!</p>
<p>Okay, here we go.</p>
<p>h''(x)= -4cos(2x) + 2sin(x) = -4(1-2sin^2(x)) + 2sin(x) = -4 + 8sin^2(x) + 2sin(x) = 4sin^2(x) + sin(x) - 2 = 0 </p>
<p>Solve for sin(x) using quad. form., then you have a graphical analysis (as you have inflection points and concavity).</p>
<p>There we go! Baelor has answered my question IN FULL, and I thank him dearly. Good Luck Baelor!</p>