<p>Hi can somebody help me with these 2 problems please?!</p>
<ol>
<li><p>The area of the region bounded by the graphs of y=arctanx and y=4-x^2 is approximately....</p></li>
<li><p>The slope of the curve y=x^2-e^x at its point of inflection is....</p></li>
</ol>
<p>Also, if you are given the graph of f(x) but you have to determine if f(x) is increasing at x=4 or not, how do you figure out the slope for that? </p>
<p>THanks soo much in advance!</p>
<p>actually for the 3rd question, i meant the following…</p>
<p>YOu are given the graphs of f and g.
h(x)=f(g(x))</p>
<p>THe questions asks if the following statements are true:
<p>How do i do this problem?</p>
<p>can somebody please help?
i’m really having trouble with these :(</p>
<p>For #2, use the double derivative and the second derivative test to find where the POI occurs. Plug that x-value into the first derivative to get the slope of the curve at that point (the POI).</p>
<p>yea…i did that and got a final answer of ln4-2 but the actual answer is supposed to be 2-ln4…i just don’t know why my answer is wrong</p>
<p>Not sure about #1, but for #2:</p>
<p>y’=2x-e^x
y’'=2-e^x</p>
<p>0=2-e^x
e^x=2</p>
<p>ln2=x this is where inflection point is.</p>
<p>Then plug back into y’=2(ln2)-e^(ln2)
Simplify: ln4-2</p>
<p>^^haha I just realized I gave you the wrong answer. Whoops.
Let me try to work it again.</p>
<p>Ok–I’m at a loss for #2 as well.</p>
<p>For #3, plug the equation for g into the equation for f. Take derivative, plug in x=4 and if it is positive, increasing, if y is negative, it is decreasing.</p>
<p>Horizontal tangents occur when the derivative equals zero. Place x=1 into the equation of the derivative and see if the y’ is zero.</p>
<p>it’s ok lol.</p>
<p>for number 3, i’m just not sure how you’re supposed to find the derivative from the graph.
Because since the graphs are of f and g, the y values are not the derivatives…</p>
<p>Wait actually, if you’re trying to find f’(4) and you go to the x-axis on the graph where the 4 is…and then find that the y-value is 3, does that indicate the graph is increasing…thus the first derivative is postive (3 is greater than 0)?</p>
<p>ahhh i’m sorry to sound so confusing.</p>
<p>i just don’t know how you’re supposed to figure out the derivative of h (to see if it’s increasing or not) if you only have the graphs of f and g and NOT the graphs of the derivatives of f and g…</p>
<p>actually can somebody just help me with this one problem?</p>
<ol>
<li>The slope of the curve y=x^2-e^x at its point of inflection is
(is the answer key’s answer of 2-ln4 the same thing as my answer of ln4-2?)</li>
</ol>
<p>thx:]</p>
<p>^I got the same answer as you did. To answer your question, they are not equivalent; one is the negative of the other. Your answer key is just probably wrong.</p>
<p>k thanks :)</p>
<p>can someone help me with this next one please?</p>
<p>Consider the function f defined on the domain -0.5 is less than or equal to x which is less than or equal to 0.5 with f(0)=1, and the limit of [f(x+h)-f(x)]/h (the limit definition) = (sec(3x))^2. Evaluate the integral of f(x)dx from the interval 0 to 0.5.</p>
<p>Thanks!</p>