Answers Chapter 4:

Section 4.3

#6 blue function=F; black function=f

#8 parabola that opens upward

#10 f(x)=1 if x>2; f(x)=-1 if x<2

#12      a. x=3 and x=-3

            b. inc. on (-infty, -3) and (3, infty); decreasing on (-3, 3)

            c. relative min on (3, -16); rel max on (-3, 20)

            d. second-order crtical point: x=0; conc up (0, infty); conc dn on (-infty, 0)

#16      a. x=1, -1

            b. inc on (-infty, -10 and (1, infty); dec on (-1, 0) and (0,1)

            c. crtical pts (-1, -2) (max) and (1, 2) (min)

            d. no second-order crti pts; coc up for x>0 and conc dn for x<0

#18      a. x=e^-1

            b. inc on (e^-1, infty); dec on (0, e^-1)

            c. crti pt (e^-1, -e^-1) (rel min)

            d. no second order crti pt; conc up on (0, infty)

#36 Critical  numbers: -1, 1; rel max at -1; rel min at x=1

#38 Crt numbers: 1, 2; rel min at x=2

#40 rel min at x=1; rel max at -2

 

 

Section 4.4

# 48answers may vary