vob - Humboldt State...
6
o vob 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'b hcx) = X . br "' a' k) =z J e *t*qx-.| e.4c-a-!l<, f-t,6+, ff ) = I . \hrff' S.+.,., F€ J L X + /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"
Transcript of vob - Humboldt State...
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'*
