Local Min/Max Values
Look at the graph and find the local or abs min/max
[(x,y) value]
Abs Max: (2,3)
f(x)=5x+2/3x-4
x=+4/3 and x=-4/3
s(t)= 10x^4+24x^3+4x^2+6x+32
Find the velocity equation
v(t)=40x^3+72x^2+8x+6
True or False
absolute max and min must occur at a critical point or at an endpoint
True
Look at the following graphs. Find the local Min/Max Values.
Abs Min: (3,1)
12x^3+10x^2+4
x=0 and x=-5/9
f(x)=10x^5+5x^3+3x^2+21
Find the velocity and acceleration equation
v(t)=5x^4+15x^2+6x
a(t)=200x^3+30x+6
Look at the following graph. Find the local Min/Max Values.
Tell me what you are finding whether it is abs max or abs min.
Abs max at (4,15)
Look at the following graphs. Find the local Min/Max Values.
Abs Max: (2,3)
Abs Min: (0,-1)
3x^4-20x^3+14
x=0 and x=5
The position equation goes as follows: 2x^7+16x^5+17x
Find the average velocity of the object over the interval t=1 and t=2 sec.
Average Velocity =2,082 ms/s
g(x) = 3x^2 - 24x + 43
Find the local extrema
Local minimum at (4, -5)
Look at the following graphs. Find the local Min/Max Values.
The [x,y] value
Abs Min: (0,0)
Abs Max: (-2,-4)
f(x)=x^2-5x+4/x^2+4
x=+2 or x=-2
s(t)= 7x^3-3x+8
A) Construct a position equation based off the velocity equation.
s(t)=7/4x^4-3/2x^2+8x+c
Double Jeopardy
An object is dropped from the second highest floor of the Sears Tower, 1542 feet off the ground. The position equation goes as follows:
s(t)= -16t^2+1542
A) Construct a velocity equation based off the position equation.
B) Calculate average velocity of the object over the interval t=2 and t=3 sec.
C) Compute the velocity of the object 1,2, and 3 seconds after it is released.
Double Jeopardy
A) v(t)=-32t
B) -80 ft/sec
C) v(1)= -32 ft/sec
v(2)= -64 ft/sec
v(3)= -96 ft/sec
Look at the following graphs. Find the Abs Min/Max Values.
Abs Max: (0,3)
Abs Min: (-3,-2)
x^2+3x/x+4
x=-2 and x=-6
Double Jeopardy
A ball is thrown straight up 6ft from the ground. (It is released 6 ft above the ground.) When it is released it is traveling at the rate of 100 ft per second.
A) If the velocity function is: v(t)= -32ft +100, what will be the position function.
B) How high will the ball go?
C)How long does it take for the ball to reach the ground?
Double Jeopardy
A) s(t)= -16t^2+100t+6
B) 162.25 ft
C) 6.309
g(x)=x^3-8x
Local Max at (-1.6,8.7)