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First & Second Derivative Tests
Definite Integrals
Indefinite Integrals
Particle Motion
Mixed Bag
100
Discovered from using the Second Derivative Test
What are Inflection Points
100
Identify the answer to the following property: a ∫ f(x) dx a
What is F(a) - F(a) = 0
100
________ is added when finalizing your answer
What is + c (constant)
100
The function found when deriving the particle's velocity
What is Particle Acceleration
100
Differentiate using chain rule: f(x) = (3x +1)^2
What is 6 (3x+1)
200
True or False: Critical Numbers cannot help you find the extrema in a graph.
What is False
200
Show the function when f(x) is an even on the integral of [-5,5]
What is 5 0 2*∫f(x)dx OR 2* ∫f(x)dx 0 -5
200
∫(4x + 2)
What is 4x+c
200
Set up the equation to find a particle's total distance on the interval [3, 9]
What is 9 ∫ |v(t)| = p(9) - p(3) 3
200
Find the equation for using a trapezoidal approximation on the integral of [1,3] on intervals of lengths of 1
What is [1/2*1(f(1)+f(2))] + [1/2*1(f(2)+f(3))]
300
Find the critical number(s) for the function: f(x) = x^3 - 4
What is 0
300
Applying Definite Integrals to Particle Motion 5 ∫a(t)dt = ? 2
What is v(5)-v(2)
300
Solve: ∫12/x
What is 12 lnx +c
300
The antiderivative of the velocity function
What is Position Function
300
Differentiate using chain rule: f(x) = sin(5x)
What is 5 cos(5x)
400
Find where the graph is increasing or decreasing: f (x) =x^2 - 4x
What is (-∞,2) is Decreasing and (2,∞) is Increasing
400
Given that 6 6 ∫f(x)dx= 45 & ∫g(x)dx= 36 2 2 Find 6 ∫[f(x) + g(x)]dx 2
What is 81
400
Solve: ∫(x^4+3x+4/ x)dx
What is x^4/4 + 3x + 4lnx + c
400
1 b 1 v(b) - v(a) ---- ∫ a(t) dt = ---- * ------------- b-a a b-a b-a
What is Average Acceleration
400
Estimate the slope of f(x)= x^2 +2 at x=3
What is about +3
500
Find the concavity of this function: f (x) = x^3 - 4
What is Concave Down (-∞,0) and Concave Up (0,∞)
500
K represents a ________ in this function and what is the done with K in this function
What is a constant & b K *∫ f(x) dx a
500
Solve: ∫x^5 - sinx
What is 1/6 x^6 + cosx +c
500
Find the net distance the particle travels with the velocity of v(t)= 30-2t between the time of 30 to 45 seconds (cm)
What is -675 cm
500
Find the third derivative of f(x) = 5x^4 − 3x^3 + 7x^2 − 9x + 2
What is 120x-18