The document contains solutions to calculus problems involving finding maximum and minimum values of functions, determining critical points, and investigating functions for maxima and minima. Several functions are given as examples, including f(x)=x^3-6x^2+12x-3, f(x)=e^x +2cosx+ e^-x, and f(x)=sin(x)(1+cos(x))^. The document examines these functions and discusses determining critical points and maxima/minima values.

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7. q.ft1wa St-aqi, 8bh
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Eq'R3"t )e3 _f (*)= et + Zcosx + e-^ rfls.lrd1-1 Efr$:flr
[Examine the function f (*)=e. +2cosx+ e-., for
val ues]
sm !r{ r

10. Frflfw E:1'nn " Ce"e
)= 2xr -9xr + 12 -3 qti-RF< .{fr8qtq e<( FTFi6TFT fi.ftr oa"r
[Find the maximum and minimum values of the function
ofthefunction f(x)=xi-5xt+5x3-ll,,,'r ffi5pve
x)=5xt' +18x5 +l5x{ -1g q{irllFcqs qfrrTn e<( qfurh{rd
rtER iF-( r I Investigate for what values " of x,
+18x5 +l5xa *l0has the maxi
s.I
r(*): 2x3 - 9xr +tz-31 ufr )tqs,us
,
Nfrfu rrt(,H8<
'fR6flq, .qr( qfrt$q wi-Elutl ,, iEiro
{ ft)= x't - 5x{ + 5x
j
- I [Discuss the maximum arrci nrinimum
,' .. r ]
fl<.RE<
e< r I Discuss the maximurn and mini
function f(x)= x-' -3x' + 3x + I I
,i,;i J:
'.:,!:d..:ri:
+5 ,{l
o) cRXls.6r",.x
qnq r I Plpve that .l'(.r)=sin.u(l+cos,r.)' haS, a maximunt, r
'rrltrc
lor.
^
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)blb
ffirya'i'*u,
cr f (x)= x3 -6xr il2x -3 e< ,ffr&{1q TfFrqfle
'/*,
t Show that f(x)=*l-o*'i ii-t
maximum nor a minimuml
,/7
>>/m,t;rs c< f (x )= x3 - 3x
3
+ 6x
,/
' nR [Show rhar f(x)= x:
maximum nor a minimum value]