Question

Step 6 So ultimately the crux of the matter is to find antiderivatives for these two functions The former is one you should already have an idea for (from your experience with calculating derivatives of inverse trigonometric functions). The latter is analogous, but can be dealt with by a useful trick you may have seen in precalculus: Find real numbers A and B to make this true, then use it to give an antiderivative for Notes on polynomial division will help refresh your memory of the precalculus involved here OK, now use the procedure you've cobbled together to find antiderivatives for 2.9(x) Note: If you simply write down an antiderivative without showing the steps as outlined above (or explaining procedure using your precaleulus and calculus knowledge, giving the reasoning to guarantee that it always works for the specified class of functions. It is not an exercise in how to use Wolfram Alpha. why a step isn't necessary), you will get ZERO credit. The problem here is to work out a Check your answers by finding their derivative. 2 An important differential equation Show that the only solutions of the differential equation ' 4y are the ones you'd expect. Which are those? (A solution of y - 4y is simply a function f with f' -4j.) Hint: show that the quotient of an arbitrary solution divided the solution you expect (or one of them) must be constant. Graphs of cubic polynomials 3 Make a graph of the function f(x)+2z +1. Give peaks, valleys, point(s) of inflection (both z and y coordinates of all these "landmark" points), intervals of increase/decrease, and turning direction (aka concavity/convexity).

Answer 1

스-o ん び

Tontdn ㄥ A- 2 x + 1 (Xtij+ 스 トt \ (7 x -1 90 n'tl (a-b)

h (%) = ant て 13 ( (x32)

aye dn + 2 (x+3) 2(저)) n1443 22- 6 Artidnivative cf虹リ 4