Department of Mathematics & Statistics
Inst: Dr. Rahman
MAC 2233/SP07-, EXAM 2 REVIEW/SAMPLE PROBLEMS(SP)
SP1.(a) Find the derivative:
(i )

d
d 
1
d  2x  1 
d
 2
, (iv )
( 3x  2 ), (ii )

, (iii )
(3x  1) 4 ( x 2  x  1) 3


dx
dx  3x  2 
dx  x  1 
dx

(b) Section 3.3--# 4, 6,7, 30
© Section 3.4- Ex 6, 8, 10, Example 5, Example 6
SP2.(a) Find the equation of the tangent line at x  1 on y 
5  4x .
y  f ( x)  (5 x 2  6) 20 calculate f ( x) .
x
(c) Explain why f ( x) 
is always decreasing.
4x  3
6
2
(d) Explain why the graph of y  5 x  2 is always concave up.
x
(b) For
SP3. For y  f ( x)  8  6 x  x , answer the following:
(a) When is the function (i) increasing? (ii) decreasing?
(b) When is the graph (i) concave up? (ii) concave down?
(c) Find the point of inflection.
(d) Find relative max and relative min.
(e) Draw the graph for  2  x  6.
2
3
SP4. Find the intervals where the graphs of the following functions are concave up and the
intervals where concave down:
(i ) f ( x)  6 x  x 2
(iii ) F ( x) 
(ii ) g ( x)  x 2 
1
x2
1 4
x  x 3  5 x  10
4
SP5. Find relative max and relative min for
y  f ( x)  x 3  3x 2  10 .
SP6 (a) A company manufactures x televisions per month.
The cos t function C ( x) 100,000  100 x and
x
the unit sale price  p  500 
( 0  x  10,000 ).
20
How many televisions must be manufactured every month for maximum profit?
And what is the maximum profit?
(b) Section 4.3—12, 22, 41, 42; Section 4.4(Optimization)—Exercise 48; Section 4.5(Optimization)Example 1(page 316), Exercise- # 6,8,15
