7. (10 pointa) Cirele \"Tue for oach statenen tht that /(z) is an absolute maxim

Question

7. (10 pointa) Cirele "Tue for oach statenen tht that /(z) is an absolute maximum. (b) True False If a function does not satinty the hypothmes of Roille's theorem dn an Inierval lo. then there is no r value in the interval (a, at which the corresponding tangent line ls horaontal (c) If f is differentiable on an interval (s,b) nnd it has alocal musinn m na?piul d The False in (a, 6) then f()o (d) True False The rectangle with fixed perimeter that masximizes area must be a sute (e) True False I (a)- 0, then (a, f(a) is an inflection point of fx) (f) True! False| Byl'Hospital's ruse limo sun-=limT-coss-1. (e) True False The point on the line y 4-x that is closest to the origin is (2.2) (h) True l Fale l Equation?3-15?+3 = 0 has at most one root in the interval 1-23, () True False If f and g are increasing on an interval I, then fg is increasing on I. ) True False In 15 minutes a car covers a distance of 20 miles between the toll booths on a toll highway with a speed limit of 70mph. The mean value theorem can be used to pove that the driver was speeding at least at one point of the road

Explanation / Answer

a) True since continuous function on a compact set attain its bounds.

b) False since Rolles Theorem is a sufficient condition not necessary.

c) True since it may be the case that function is not differentiable at that point

d) True

e) False

f) True

g) True

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