Name:
Exam 3 Guide :: Math 271 :: March 18, 2016
1.
The figure above is the graph of the derivative of a function f (x).
Find the inflection points of f (x)
and state where f (x) is concave up
and state where f (x) is concave down
2. Consider the function f (x) = x5 e8x on [-2,4].
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
3. Consider the function f (x) = x3
6x2
63x + 11 on [-5,12].
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
4. Consider the function f (x) = 7e4x
3
4x
on [-2,1].
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
Page 2
5. Consider the function f (x) = x sin(2x) on [0,
3⇡
].
2
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
6. Consider the function f (x) = 6(x2
1)2 on [-1,2].
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
The inflection points are
The function is concave up on the interval
The function is concave down on the interval
Page 3
7. Consider the function f (x) =
x4
2x3 + 4x + 2.
Find any inflection points of f (x)
The function is concave up on the interval
The function is concave down on the interval
8. A ball is thrown upward, its height above the ground in feet after t seconds is
h(t) =
16t2 + 46t + 5
Find the time that the ball reaches it maximum height.
Find the maximum height of the ball
What is the acceleration of the ball after 1 second?
Page 4
9. If an arrow is shot straight upward on the moon with a velocity of 68 m/s, its height (in
meters) after t seconds is given by
s(t) = 68t
0.83t2 .
What is the velocity of the arrow after 9 seconds?
How long will it take for the arrow to return and hit the moon?
10. A box with an open top is to be constructed from a rectangular piece of cardboard with
dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then
folding up the sides.
Find a function that models the volume of the box
Find the largest volume that such a box can have.
Page 5
Name:
Exam 3 Guide :: Math 271 :: March 18, 2016
1.
The figure above is the graph of the derivative of a function f (x).
Find the inflection points of f (x)
and state where f (x) is concave up
and state where f (x) is concave down
2. Consider the function f (x) = x5 e8x on [-2,4].
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
3. Consider the function f (x) = x3
6x2
63x + 11 on [-5,12].
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
4. Consider the function f (x) = 7e4x
3
4x
on [-2,1].
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
Page 2
5. Consider the function f (x) = x sin(2x) on [0,
3⇡
].
2
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
6. Consider the function f (x) = 6(x2
1)2 on [-1,2].
The absolute maximum value is
and it occurs at x =
The absolute minimum value is
and it occurs at x =
The inflection points are
The function is concave up on the interval
The function is concave down on the interval
Page 3
7. Consider the function f (x) =
x4
2x3 + 4x + 2.
Find any inflection points of f (x)
The function is concave up on the interval
The function is concave down on the interval
8. A ball is thrown upward, its height above the ground in feet after t seconds is
h(t) =
16t2 + 46t + 5
Find the time that the ball reaches it maximum height.
Find the maximum height of the ball
What is the acceleration of the ball after 1 second?
Page 4
9. If an arrow is shot straight upward on the moon with a velocity of 68 m/s, its height (in
meters) after t seconds is given by
s(t) = 68t
0.83t2 .
What is the velocity of the arrow after 9 seconds?
How long will it take for the arrow to return and hit the moon?
10. A box with an open top is to be constructed from a rectangular piece of cardboard with
dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then
folding up the sides.
Find a function that models the volume of the box
Find the largest volume that such a box can have.
Page 5