Find the Critical Points
Graph Questions
First Derivative Test
Second Derivative Test
Particle Motion
100
What's the derivative of Amazon with respect to cost of shipping?
Amazon Prime!
100
Why are you not allowed to do calculus while intoxicated?
Because you can't drink and derive
100
Why can't you solve every problem with calculus?
It has limits!
100
What is an opinion without 3.14159?
an onion!
100
What do baby parabolas drink?
Quadratic Formula!
200
How do you find critical points from the function?
Take the derivative, find the zeros, and figure out x values you can't plug in.
In a fraction set numerator and denominator equal to zero separately.
200
Given the graph of the first derivative, how do you identify the critical points?
The zeros on the graph
200
What does the sign of f’(x) (i.e. the first derivative) tell you about f?
Increasing or Decreasing
+ -> increasing
- -> decreasing
200
What does the sign of f’’(x) (i.e. the second derivative) tell you about f?
Concavity
+-> CCU -> min
- -> CCD -> max
200
What does the meaning of + and - change to in the first derivative test for particle motion?
+ is moving right (not inc)
- is moving left (not dec)
300
Find the critical points of
f(x)=3x5-20x3
x=0,2
300
Given the graph of the first derivative, how do you identify the points of inflection (where concavity changes) of the original function?
The maximums, minimums and sharp turns.
Basically how we find critical points on the original graph.
300
If f'(x) goes from + to - around a critical point then the critical point is a _______
Maximum
300
If f''(c)>0, then f has a _____ at x=c.
Minimum
300
What does the meaning of + and - change to in the second derivative test for particle motion?
+ is slowing down (not CCU-> min)
- is speeding up (not CCD->max)
400
Find the critical points of
f(x)=(x-1)2 (x+3)
x=1, x=-3, x=0
400
if this is the graph of f'(x) what are the critical points of the original function?
x= -3, -0.5, 2
400
Use the first derivative test to find the relative extrema of the function
f(x)=3x^4 + 5x^3
min (-5/4, -2.441), no max
400
Use the second derivative test to find relative extrema of
f(x)=3x^2 + 4x - 1
minimum (-2/3 , -7/3)
400
A particle moves along the x-axis with the position function given below. Use a chart to describe the direction of the particle. (Left or Right?)
2/3t^3-2t^2
where t>0
moving left from 0 to 2
moving right from 2 on
500
Find the critical points of
f(x)=x^3/(x+5
x= 0, x=-15/2 and x=-5
500
If this is the graph of f'(x) what are the inflection points (where concavity changes) of the original function?
x=-2, 1
500
Use the first derivative test to find the relative extrema of the function
f(x)=1/3x^3+x^2+7
-2 is a max
0 is a min
500
Find the relative extrema of
f(x)=x^3 - 3x^2 - 9x
using the second derivative test.
f''(3) = 12 -> min
f''(-1)= -12 -> max
500
A particle moves along the x-axis with the position function given below. Use a chart to describe the direction of the particle. (Left or Right?) Then use the second derivative to describe the speed of the particle.
1/3t^3-7/2t^2+12t-5
where t>0
moving right 0 to 3
moving left 3 to 4
moving right 4 on
Speeding up until t=7/2
slowing down after t=7/2