ovob

Differentiate the following functions. No simplifying. Take derivative and stop.

a. .f (*):4'-3xa,.3-er, *roe : -:: Zxa + 2 x-;- p3x+,(qrK

t'fd =,1.n Q .Llx - lL{- t2x-1- zt*.2 +

o *6n ?Qtb"t*c4-rd'bhcx) = X . br "'

a' k) =zJe *t*qx-.|

e.4c-a-!l<,

f-t,6+, ff ) =I . \hrff'

S.+.,., F€ J

LX

+ /rx y'2'.2

r. s(t)=!* (Woho* rvl@H -Q* tr)(l*-hs,st

Practice Problems Exam 3

l.

t-TM

(tun+v)

e. n(r) = e2'lnx a

h'k) =-e'r

.(s* #)Sx* {T te

3t&)= (* +.s"

@

2. Use the second derivative test to identiff the relative maxima and./or minima.f(x)= x4 'Zxz +3

lrr)=t*l x3-gxD = ,lx(xa- t)

e = ex(K+()(K-()_[ X=u x:t ft ep

€ "(*)= l}x'-\{"/r) = -q lo :

f "€t) = tL (t t)'-V= tz-1_'Ij'

,p (r t) ' 1',)q - 2 (rr;'+ 3

= -l+;--L

3. Find all vertical and horizontal asymptotes (if they exist) using CALCULUS techniques.?, , x+2 x+4_ yt -3,-L

it^ Ta\rs \i;'irf *. tn"r'l-?Ctt',,r'Y---7 ^ / tvtts tL .^: - -, x*z "^[ li*" "\]Xi #6)

lrry / =it;# /'-T= g ( =)Kft \ ,'=o / =+;rt {NovA@x=-2

lct*)i1/1ttA-5t^ *^

(r,z\ 1t-t,z)aJY ( r e-G*'l/e*

VVt r n iumx

Vl,.av c t\ t'r'aA\vnSttolc

.tYt - -/A. ^'

-'/

G

4' Find the extrema fabsorute maxima and minima] of the function.r / a. "f (x) -.x5 - Sxa +1 on the interval 0 s ,r s 5{ t/r) = sK{ :2oxL.

v'rlr;r'"'E&

) =€x'(x-l) X=cSVt.=o X-q--o |io\ = t

K3= 6 X:9X=o

'\ ' (o't)

@X=O

{ (o)= |

(or l)

x4i(q) ,.llscqf{ I

= tyztl -S(zs$+t= 1oz*-lz9Ott= -2Y6+l= -zStr(q,-z ss)) m)w-f

11,\J* ilpsQlo/- !{/..'U( t vh\rpL-'s 4* ?3r<,12s) a'"at

+1,rL atbEo Wl-4* Vvlrn lryl.ttn

1s ^* (or - PLq).

K=S

+^. a'VSrsV-)W tn^s,.Xi W^rr^nl =- {

'rS L tu,ot, occrJrS ",t I LS, l)/ ,1'

0 a"e\ S. ) '/\"o\x

al -3 s x s2

+(-3) = (. )'-q)t= e_u)s

= 3e{(-t 3r zs)

N rryrotX

X= 2-

f(r-l = (r'-u)t=Q

(z,u\

fl^{- duxc:u.rk w'r tn'*,^,^ I Pfg) = SLs(s)Y+t \t s ^* (q, -z\T) a,,*!" / = Ttzd- TPrtl

tt'

-T.TG)=( *, -4)" on the interv'/r) = ! (x'-..{)t(zx)(v) = lox (xr-q)t0 = [ox i1L.{)YJDy =o (XL,,-1)q= ox=o x L,{ =o

K'-- q

X =Jtfi-\-*tL

C'r;h-c'{ %)^+X=O

fr {o) = tq)s= - lozq

( D t -,o?,*aX-- -2

f i;)= (,-r.-r)"-_o

Cz,o;

oid"

€Mporin4,

t'(x)= ;1'*t= \ O= 2x&'-.){,,/r)= rfloi}(-zu) -(-:'n,)(rc-'o'l 'd V;:Z -;''

qy'+t){ ,..1.r X=t-r x=!,f.,

Recall, f (x) =;Jd' Find the inflection point(s), if any, and thejglgryals where the function is concave upand concave down.

e. sketch a fatly accurate graph of f(x) based on the information in phrir'uq

(t, * ) v^-')c

IPXrG

lr"6ty, (- l, ;r,)wrl\

6. Find the equation of the tangent line at the specific point.f (x) = (x +l)e-z',; _where x = 0OwLr*FvJ*

{,/x) : ;, ; nwtr; -i_,. r,j ('v1"' I (D, I

= e-z- (2 6*r)+ l) -lx+t

h-q) F-'l Il c.'[ - u* e* "'lQ"J- L ,t*:'q* ''-,-

-f-;--2x"-2ttf -w ZT\; I ,r? 7

@+D''ffi = ffi v,ilprth,. t''fl ;i';,'itn'ji;= "

t f,(o)=lco) =tN{,"xa

n -2KtL

= !--2*(-zx- 2+t)(- zx - |

O\ACgvu-z- YQc, o) u(rle r s)

Q ctn @r^-a* dqrr",*(-@,- 6 )U Co, ,tT)

\ n{4"r'k-.- 9*

li'*