Find the gradient of the curve x^3 + y^3 = 4y^2 at the point (2, 2).
dy/dx = 3
100
Find the greatest value of y = x^3 - 5x^2 + 7x on [0, 4].
y(max) = 12, when x = 1
100
The most prevalent speed limit in the US.
What is 45 MPH
100
Find dy/dx, if y^2 = tan2x + sec 2x.
dy/dx = y sec2x
200
Given that f(x) = 3x + 2 + 1/x, find f"(-1).
-2
200
The largest stadium in the Unites States
What is Michigan Stadium in Ann Arbor, Michigan
200
A particle moves along a straight line so that its velocity v when it is s meters from a fixed point is given by v = s^2 + 3. Find an expression for its acceleration in terms of s.
a = 2s(s^2 + 3)
200
Water is being poured into a conical vessel at a rate of 10 cm^3/s. After t seconds, the volume V of the water in the vessel is given by V = (Pi/6)x^3, where x is the depth of the water in cm. Find, in terms of x, the rate at which the water is rising.
What is Willis Tower (formerly known as the Sears Tower)
300
The youngest U.S. president at time of inauguration
Who is Theodore Roosevelt (42 years old)
300
A 10 M long ladder is leaning against a wall. It starts to slip away from the wall at a rate of approximately 2/3 M/s. How fast is the top of the ladder sliding down the wall when the foot of the ladder is 6 M from the wall?
What is .5 M/s
300
Find dy/dx, given that y = 2^x.
dy / dx = 2^x ln2
400
Find dy/dx is y = (x + 4) * (x^2 - 1)^0.5
(2x^2 + 4x - 1) / (x^2 - 1)^0.5
400
The four largest cities within the United States, by population (order does not matter)
What are New York (1), Los Angeles (2), Chicago (3), Houston (4)
400
Find the x-coordinate of the maximum of f(x)=2x^4-4x^2+1
What is x=0
400
A piece of paper is burning around the edges of a circular hole. After t seconds, the radius (r cm) of the whole is increasing at the rate of 0.5 cm/s. Find the rate at which the area of the whole is increasing when the radius is 5 cm.
What is 15.7 cm^2/s
400
Find the derivative of f(x)=(e^x)Sin(2x)
What is (e^x)Sin(2x)+(e^x)Cos(2x)(2)
500
Find the value of dy/dx at x = 0, given that y^3 - xy^2 - x^3 = 1.
1/3
500
The highest domestic grossing film of 2012
What is Marvel's The Avengers
500
Find the coordinates of the minimum point on f(x)=x^4+2x^3
What is (-3/2 , -27/16)
500
A reef 120 M from a straight shoreline is marked by a beacon which rotates six times per minute. How fast is the beam moving along the shoreline at the moment when the light beam and the shoreline are at right angles? (Provide answer in M/sec)