MAT137Y1 Lecture : MAT 137Y 2007-08Winter Session, Self Generated Solutions to Problem Set 8.pdf

• School: UTSG
• Department: Mathematics
• Course: MAT137Y1
• Professor: all

Document Summary

Mat 137y 2007-08 winter session, solutions to problem set 8. 1 (i) for f (x) = (x2 1)3, the derivative is f (cid:48)(x) = 6x(x2 1), so the critical points are x = 0, 1 and the endpoints are x = 1,2. For the local extrema, we see that f (cid:48)(x) > 0 when x ( 1,0) (1, ) and f (cid:48)(x) < 0 when x ( , 1) (0,1). Hence local minima occur at the points ( 1,0) and (1,0) and (0, 1). For absolute extrema we compare the values of the function at the endpoints and critical points. 6 > 0, fore there are no local extrema. Looking at the endpoints, f (0) = 2 and f ( so the absolute minimum is at x = 0 and the absolute maximum is at x = . 2 (she 4. 3: suppose f (x) = ax2 + bx +c.