Let f(x)=xex22f(x)=xex22.

(a) Find the domain, intercepts, and horizontal and vertical asymptotes of the function. If an intercept or asymptote does not exist, state it.

(b) Given that f(x)=(1x2)ex22f(x)=(1x2)ex22, find the critical points, intervals where ff is increasing and decreasing, and the extreme values indicating which is a max or min.

(c) Given that f(x)=(x33x)ex22f(x)=(x33x)ex22, find the intervals of concavity and inflection points of ff.

(d) Sketch the graph of the function. Label any intercepts, asymptotes, extreme values, and inflection points.

2 Let f(m) = weeT. (a) Find the domain, intercepts, and horizontal and vertical asymptotes of the function. If an intercept or asymptote does not exist, state it. $2 (b) Given that f'(m) = (1 m2)e_7 , find the critical points, intervals where f is increasing and decreasing, and the extreme values indicating which is a max or min. 2 (c) Given that f"(m) = (m3 3m)e_37 , find the intervals of concavity and inflection points of f. (d) Sketch the graph of the function. Label any intercepts, asymptotes, extreme values, and inflection points