MATH22L CALCULUS I 100pts TEST 2 Spring'l1Page 1

6pts 1. Is f (x) continuous at x :fr? (show work) ft>rl = It

Ft:,;S-- 3r#) * g = I <i,s*s.,'

{,11 ft:&j i: \ .lx,$'< ur

INSTRUCTOR: CARLAMORRISNAME: *'l ,l-l

II

J

3x-52^x -Jx+zx-2

x=2

x+2

Crt x*lS[r)" \*J}"4= 0

t -ai,* $B)= r,x)t

O=o',*fu*-\

IN PROBLEMS 2-5 FIND THE INDICATED DERIVATIVES (5PTS EACH)

3. f '(t) if f(t): (6t5 + 4t3 + 3114s

*{ct,,b4. d ldt 15a6t5 + lb3t31-!ct2 - zt1-*11 5. d2ldr2 1813 + 7r2 + 9r + 6) I .:,

dVrs*tili.rQ,"*' 73r + lq) lt,_i

f-t ntL*1es-J

{i;,+{;e6 ?tb3+?

5pts 6. Find the equation of the tangent line to the curve (x) : 7x2 + 5x -t 7 at x : 2

Vb) -, Cg + u:*"t = ,.+.S p+ ( a,ris)

I tO .- tt-txt5\'($ = 33. rn

L' I J I \

t : -\i^. I , \ \( r *.J \.-l

j

Spts 7. Sketch the graph of a function that has the following properties, f '13; : 0; f (3) : 1, f(0) :concave up for all x.

-.e@bi(t i, i10pts S.Locate all possible extrema of f(x) : (113) *3 + 4x2 + l2x.Also check for concavity and

inflection points. Give intervals for increasing, decreasing, concavity, etc and then Sketchthe graph. I

*{! t,r.-uCl.,, {! /'t-' t

O$'(e)=o?('fi, i

f(o), r:

nc/Y G ArO

$tib"Llt rnn fr al -E

'i\t-{a*s -\'r

'--T---*?Con r,-|-oufr t %-9

.dat,6 W "rO{ tnpp* 8/,

@ t{Y= *'(Y.1 li),x

f Al = *+trY+ t7(./+*Yv+ d

x+2" +v+a++'rt,

@ ie -z@

lne (-d)t*b)UCA,&

&c (-6,-8

fi*s ;^r,1h 'm6X\ f*,!;j/qt)<rpt,(q rol (i frdC* uf oe! 'T- 860)l)rrirJ

tf:+'

1

rf

')

)

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MATH22L CALCULUS I 100pts TEST 2 Spring'l 1 INSTRUCTOR: CARLA MORRISPage2 NAME: l-,: ,r-l

10pts 9. Graph (") : *o - 2*' by finding the x and y intercepts, relative extrema, inflectionpoints, intervals increasing or decreasing and intervals of concavity

&z Wrd- {'ifiP d'

8pts 10. Find the minimum value of f(t) : 1013 - 15lP + 7,t> 0 and give the value of t wherethis minimum occurs. i** li *-ie)fs'*fft t t

w(t-t) fT-r# ;*\or--)i{J) i rl,.r i,u,,,' ,,,i.1/Lt,7 1{\\)7i ;?;i,1 fi* l-={ \-

- €10pts 11. Suppose amanhas $720 build a rectangular enclosure. The north and south sides of the

enclosure cost sides cost $6 per running yard while the east and west sides which are moreexpensive more cost $9 per running yard. Find the dimensions of the enclosure that willmaximize the area of the enclosure.

lrh+ 181 = 1r'{)

i\ tC"N X ({,tv

l8U -' '7eO-

t&xL{ * Q O -VrX| -- /,^{

kx)= X(qo-%k)

A{r.} = L{ct"x*%"x,

frk)- t!0*,q*xfcr-"(/:it

.L

t). -y1ct"x-

X=3*$* ao

i1^-i Ir)6+< G,te_G kn 3o{6d rao3d, ffr bff)ud

x"i''af;#(xe"a)

\.t>, t {b

$tit, {y3-(x

4>,&llxti)

Kr{"*4n*5

a,

N-(xf

de,r(-*o, D ilq\)\n( {- t3o) ,,i ( i;oa)

lcrr{ rrtrr^i (! l, _,){t-l6"og 6.r{L1z fu; O)

f "(4. raxf;-i{

f.=t

/;"f- ''

i- 1 t-1*

.f6Fi Q

jo", yr ee, qt ir(€,")C.a,,f1n..,,,- (.rq..

rdai ;)

": -i

r>--[.-;lr Jl,{/t <_Au% , -{e}'J / ',,/

MATH22L CALCULUS I 100pts TEST 2 Spring'l 1 INSTRUCTOR: CARLA MORRISPage 3 N*n, k,*l-

Spts 12. Given the cost function C(x): *'- 15*' + 100x + 150 find the minii# marginalcost Ct* , nya*g*xfto* , MC {ruf.u.*,h: s

C1.'00 -- l4C' = (ox-AO {rrt t'tt /,1 e / sks

5 ,*tin 7S*19)r \dJ

15pts 13. Suppose the consumer demand for a certain item as a function of its price p is given byx: D (p) :40 - (p l6). Determine the production level and price that maximizes theprofit if the cost output function is given by

c (x): *3 + 9*2 - 36ox + 2,ooo

c5 X -r. th

C7s ptaao

6* * av 0_rf='.Vo!pc"

Ee^J AVox -{c( e

*aco(J- Areo0

)J

Pr'E) 1

formulas

Y-Yr : m(x-x1

fill : -I lmz

Pr(x) -.Caqox 1ye {fuqg-ilox+;cdPrQ0 = -X3 * t6)P +Gogx- ae(D

- 3ry4-3cx +(o6b4(xaliox --a"g-ily{-d)(xet$

e& or>qd6) ax*by:c y:mx*b

^ =Y2 -Ylx2 -xl

Prfi$= tso<)

'meq pro€{* r /Socufug py 4d.u,ct lou.,n_{/,(il-*lYo (a ci:

x: - b*"t@ 4*

1111 : 1Il2