AB Calc FRQ question explanation?

Test Preparation AP Mathematics & Computer Science
1

<p>Can somebody please explain question 4 from the 2004 Form B AP Calc AB exam?
<a href="https://secure-media.collegeboard.org/secure/ap/pdf/calculus-ab/ap-2004-calculus-ab-scoring-guidelines-form-b.pdf?__gda__=1366416253_5db51a1e2f1c4beadce4d4da1be99490%5B/url%5D"&gt;https://secure-media.collegeboard.org/secure/ap/pdf/calculus-ab/ap-2004-calculus-ab-scoring-guidelines-form-b.pdf?__gda__=1366416253_5db51a1e2f1c4beadce4d4da1be99490&lt;/a&gt;&lt;/p>

<p>I don't get part b or c, although part a is pretty straightforward. I will give you cookies!</p>

2

<p>B is simply asking for the absolute minimum and maximum points of f(x). If you recall, those can occur at endpoints (closed interval), stationary points (zero derivative a.k.a. points 1 and 4 as shown on the graph), and rough points (undefined derivative). These are all called critical points.
So the critical points are -1, 1, 4, and 5. Look at the graph. It’s telling us the derivative is negative from -1 to 4. In other words, the function, f, is decreasing. After 4 the graph is positive and the derivative is increasing. So 4 is our absolute minimum. -1 or 5 could be our maximum. Remember, thinking in terms of our f graph, we started at -1, the graph went down (since the derivative was negative), and then quickly went back up for a bit (since the derivative was positive for x>4). So the question is, which is greater, f(-1) or f(5)? </p>

<p>C has g(x) = xf(x). Find the tangent line at x=2. First find the slope.
g’(x)=f(x)+xf’(x).
g’(2)=f(2)+2f’(2)
y-g(2)=(f(2)+2f’(2))(x-2)
2f’(2)=2(-1)=-2
f(2)=6
g(2)=2f(2)=2(6)=12
So
y-12=(4)(x-2) or y=4x+4</p>