A Calculus question?

<p>I know it's not SAT related, or in some other dimension it is, but my summer assignment for AP Calculus AB is about 25 pages long and i have a question</p>

<p>This is a link to part 1.</p>

<p><a href="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxuZXdtaWxmb3JkaHNtYXRoZGVwYXJ0bWVudHxneDo2NjNhMTNkOGNmNGFlN2Uy%5B/url%5D"&gt;https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxuZXdtaWxmb3JkaHNtYXRoZGVwYXJ0bWVudHxneDo2NjNhMTNkOGNmNGFlN2Uy&lt;/a&gt;&lt;/p>

<p>I have no idea to where to begin (for question #2!)</p>

<p>If someone can just assist me in answering 2A., I think I would be able to solve the rest. </p>

<p>Thanks!</p>

<p>Find the slope between the two points using the formula for slope: (y2-y1)/(x2-x1). To answer the second part of (a), I would draw a line connecting points (2,4) and (3,9), then draw the tangent line at (2,4). Is the tangent line steeper or less steep than the line connecting the two points?</p>

<p>Cool, I just started school (and Calc AB/BC:)) here in Arizona and am learning this.</p>

<ol>
<li><p>Take a look at this picture right here: Approaching</a> the Tangent Line</p></li>
<li><p>Producing multiple secant lines in order to approach the tangent line is what your problem is asking. Simply find the slopes using the points they give you and see how they relate to the actual tangent line at (2,4).</p></li>
</ol>

<p>So should I use the slope formula? y2-y1/x2-x1 once I draw the line? OR is there some new calculus derivative related formula im missing?</p>

<p>Nope, just use the regular slope formula. You don't need any calculus except the definition of a tangent line, since the second part of (a) asks for only a qualitative answer.</p>

<p>okay thank you! Can you tell me what your answer is (if you did it)? I want to check if mine is correct.</p>

<p>still kinda wondering how to do the last part of it? how do i draw a tangent line to the point (2,4) and know that it's right. I know that the tangent line would have to intersect the parabola once, but isnt there an array of possibilities as to where it may intersect?</p>

<p>They want the tangent line AT THAT GIVEN POINT. So your line has to just touch the parabola there and only there. When you go to draw it, you'll see that there is very little wiggle room -- everyone who draws it correctly draws NEARLY the same line. </p>

<p>Try bringing a ruler closer and closer to the parabola, attempting to touch the parabola at that point and no other. You'll see that you have to hold the ruler at a certain angle to make that happen.</p>

<p>ahhhhhhhhhhhhhhh okay! thank you!</p>