<p>Hey so I have a Calc test this week and need lengthy explained help on most of these questions basically I think my test will be set up like this but don't completely understand how to do all of this. So answers and help will be greatly appreciated:</p>
<p>Let's say this is the equation: x^3/(x^2-4)</p>
<p>Find the x-intercept, y-intercept, vertical asymptotes, horizontal asymptotic, f', increasing, decreasing, max, min, f", concave up, concave down, inflection points, and symmetry.</p>
<p>I would really like it if someone could help me soon like by tomorrow afternoon so I have time to study. You don’t have to answer every single one just the ones you know…I would really appreciate it!</p>
<p>I hope you know how to find the x- and y-intercepts of that function (that’s alg 1/2 material). Just set y or x = 0, respectively. Vertical asymptotes at x = 2, -2 (note that we do not obtain 0/0) and no horizontal asymptotes since the degree on the numerator is larger.</p>
<p>Given y = (x^3)/(x^2 - 4), use the product rule to find y’.</p>
<p>y’ = ((3x^2)(x^2 - 4) - (x^3)(2x))/(x^2 - 4)^2</p>
<p>Set y’ = 0, solve for x to find critical points (remember to test whether they’re maxima, minima, or neither). Differentiate again and do the same thing.</p>
<p>Okay I basically know everything but how to find concave up and down and inflection points. Can you explain that?</p>
<p>A differentiable function y = f(x) is concave up when y" > 0, concave down when y" < 0. Inflection points occur when the concavity changes sign (y" = 0, is negative on one direction, positive on the other).</p>