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Kouba
Worksheet 1 1 1. Determine the values of x for which the following functions are
increasing, decreasing, concave up, and conmve down. Indicate relative
maximum, relative minimum, and inﬂection points. Neatly sketch the
graph. a. f(x)=x2(x3)v b_ f(x): x 0. f(x) = 2x— 1/x d. 2. Determine a function fwhose derivative is given by f ' . a. f'(x)=1r2—e2 b. f'(x)=1+x+x2 c. f'(x) = secz7x d. f‘(x) = 25inxcosx 9 f'(X) = 3(f(X))2 X3 3. Let f(x) =
x+ 1 For whatvalues of x is f'(x) = 0 ? 4. Solution A is 35% alcohol (by volume) and solution B is 60% alcohol (by
volume). How much of each solution should be combined in order to have
two liters of solution which is 40% alcohol (by volume) ? . 5. Let f(x) = g(h(x) ). Assume that h(1) =2, g(2) =3, h'(1) =4,
g'(2) = 1/2, h"(1) = 3, and g"(2) =  2 . Determine values for each of the
following. a. f(1)
b. f‘(1)
c. f"(1) ,. 2’5 6. A circle is inscribed in the square, which
is inscribed in the right triangle, which has
height 2 and base 1 . Determine the
circumference of the circle. See diagram. 7. Wave Y‘ijor‘ous‘y +hq+ ‘Hne $oiiowim3 STq‘i'emei/d's aibou‘i' limits av‘e Jame. 4. im (3X—l):5/ b \m (q+2><)=3
Xﬁz X‘M X9‘2.
3 \im i— =1 43 hm X" :~3
Xe?) X—l X—? "i X+l
x1 i
3 hm (7— wag k hm : Ta
X—H"! xqé: [90(4'3 ...
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This note was uploaded on 11/30/2010 for the course MAT MAT 021A taught by Professor Kouba during the Winter '09 term at UC Davis.
 Winter '09
 Kouba
 Calculus

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