Concavity And The Second Derivative Test Worksheet With Answers Page 8
ADVERTISEMENT
1
2
3
4
5
6
7
8
9nd
Calculus Maximus
WS 3.4: Concavity & 2
Deriv Test
( )
3
2
=
+
+
+ , where a, b, and k are
18. A cubic polynomial function f is defined by
f x
4
x
ax
bx k
x = − , and the graph of f has a point of inflection
constants. The function f has a local minimum at
1
( )
( )
′
x = − . Find the values of a and b. (Hint: create ordered pairs satisfying
at
2
f x ,
f x
, and
( )
′′
, then solve the system of equations).
f
x
19. For each of the following, (i) identify the open intervals on which the functions are concave up or
concave down, then (ii) locate and JUSTIFY the inflection points)
[
]
( )
( )
−
4
3
2
1
=
−
−
+
+
=
−
(a)
f x
3
x
4
x
6
x
12
x
1
(b)
f x
sin
x
, on
1,1
ln x
( )
( )
2
π
=
−
≤ ≤
=
(c)
f x
cos
x
2sin , 0
x
x
2
(d)
f x
x
Page 8 of 9
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education