Differentiation 101
integration 101
Fun With Graphs
Word problems
100
What is the derivative of 3x5+x2-1?
What is: 15x4+2x
use power rule
100
What is the integral of x3+4x2?
What is: x4/3+2x3+C
∫xn=xn+1/n+C
100
What is the value of f(x) as it approaches 4?
What is: 5
the value of f(4) is 4 but has the function approaches 4 the limit value is 5
100
The equation to a car's velocity can be represented by the function v(t), where t is measured in seconds and the v(t) is measured by meters per second. If v(t)=3x4+2x3+3x, then what is the acceleration of the car when t, time is equal to 2?
What is: 123 meters per second per second (m/s2)
acceleration is the derivative of velocity
200
The derivative of a function can also be referred to as
What is: The slope of the tangent line
200
What is the area under the graph from (2,6)?
What is: 4
the integral of a function is equal to the area under the function
200
What is: 6
as h(x) approaches -3 from the left the value is 6
300
What is the derivative of 2x2/3-3x3? (without any negative exponents)
What is: -9x2+4/3x1/3
use power rule; know that x-n=1/xn
300
What is the Fundamental Theorem of Calculus?
What is:
300
True or false: The function is both continuous and differentiable on (-3,3)
False, the function is continuous on the given interval however it is not differentiable because there is a corner at x=0
300
The function of graph g(x) can be represented by the equation g(x)=x4-4x3+2. On what intervals is the function g(x) decreasing?
What is: (-
derive the function and find the critical points (where the value of the derivative is 0) then find where the derived function is positive and negative
400
If s(t)=(3x-1)(-8x2+2x), what is s'(t)?
What is: -72x2+28-2
use product rule
400
What is ∫cos(2x)dx?
What is: 1/2sin(2x)+C
integral of a trig function; there is an inside function (U)
400
What is the value of g(0)?
What is: 1
the function is approaching -2.5 but the value of g(0) is 1
500
If g(x)=3(2x)5, what is g'(x)?
What is: 15(2x)4(2) or 30(2x)4
use chain rule
500
What is ∫e-x+x2?
What is: -e-x+1/3x3
know the integral of ex
500
What is the value of f(2)?
What is: DNE (Jump Discontinuity)
500
The amount of water entering Jacob's fish tank can be represented by the function w(t), where t is time measured in seconds and w(t) is measured in gallons per second. if w(t)=9x+5 and the tank has 2 gallons of water when t=0, what is ∫w(t) when t=4?
What is: 94 gallons
if w(t) is the rate at which the amount water is increasing the integral would be the amount of water