Question

Given: ?(?) = 8/ (4−?^2) and ?(?) = sin(?) − ?. Answer the following for each of the functions given. (a) Find the domain (b) Find the intercept(s) (c) Find the asymoptote(s) (d) Find the possible critical and inflection numbers (e) Construct a sign table for Hint for (f(x), f'(x), and f'' (x) and show step by step (f) Find the intervals in which the function is increasing/decreasing (g) Find the intervals in which the function is concave up/down (h) Find the relative extrema and inflection points (i) Sketch the graph of the function

Show a complete sign chart for f(x), f"(x), and f''(x)

Answer 1

C

For f(x) , asymptote will be x=2, -2

And g(x) have no aymptotes.

D.

For finding criticsl points putting f'=0 gives

8x/(4-x^2) ^2=0 gives x=0 is the critical point.

And for inflection point putting f'' =0 gives x= √3/2,

-√3/2 are inflection points.

Now g(x) , g'(x) = cosx -1 =0 gives x= 2nπ are critical points.

And g'' =-sinx =0 gives x=nπ are inflection points.