Differentiation
Find f'(x) if f(x)=3x2+5x-7
f'(x)=6x+5
Differentiate x2+y2=25
dy/dx = -x/y
Find the critical points of
f(x) = x3 - 6x2 + 9x
x = 1 , 3
A function is defined implicitly by
x2 + y2 = 16
Find the maximum and minimum values of 𝑦.
Maximum y: 4
Minimum y: -4
Who built the ark?
Noah
Differentiate f(x)=x3+ln(x)
f'(x)=3x
Find dy/dx if x3 + y3 = 6xy
dy/dx = 6y-3x2/3y2-6x
Find the absolute extrema of
g(x) = x3 - 3x
on the interval [-2 , 2]
Absolute max at x = -1
Absolute min at x = 1
A ladder 10 ft long is leaning against a wall. If the bottom is sliding away at a rate of 2 ft/sec, how fast is the top moving down when the bottom is 6 ft from the wall?
−1.5 ft/sec
What did Jesus turn water into at the wedding in Cana?
Wine
What is g''(x) if g(x)=e2x+sin(x)
g''(x)=4e2-sin(x)
Differentiate ex+xy+sin(y)=5 implicitly
dy/dx = -ex-y/x+cos(y)
A farmer has 320 meters of fencing to enclose his land. One side of the land already has a stone wall on it. What dimensions will make the maximum area.
Width = 160 meters
Length = 80 meters
A cylindrical water tank with a fixed volume of 500 cubic meters is to be constructed. The base and top cost $10 per square meter, while the side costs $8 per square meter.
Using implicit differentiation, find the tank's radius and height that minimize the total material cost.
Radius: 3.98 meters
Height: 10.05 meters
In the Book of Exodus, what did God provide from heaven to feed the Israelites in the wilderness?
Manna
Find the derivative of f(x) if f(x) = x2/x-1
f'(x) = x(x-2)/(x-1)2
Find the second derivative of the equation
x2 + xy + y2 = 7
((x + 2y)(-2+ 2x + y / x + 2y) - (-2x - y)(1 - 2(2x + y) / x + 2y)) / (x+2y)2
A closed cylindrical can must have a volume of 1000 cm³. Find the dimensions (radius and height) that minimize the surface area.
r = 3root(500/pi)
h = 1000/pi*r2
Water is being pumped into a conical tank at a rate of 5 m³/min. The tank has a height of 10 m and a base radius of 5 m. How fast is the water level rising when the water is 4 m deep?
5/4pi/min
Which Old Testament prophet was taken to heaven in a chariot of fire without dying?
Elijah
What is the derivative of f(x)=xx
f'(x) = xx(ln(x)+1)
Differentiate sin(xy) = x2 - y2
dy/dx = (2x - ycos(xy)) / (xcos(xy) + 2y)
Find the dimensions of the rectangle with the largest possible area that can be inscribed in the ellipse (x2/a2) + (y2/b2) = 1.
sqrt(2)a by sqrt(2)b
A spherical balloon is being inflated at a rate of 10 cm³/sec. How fast is its surface area increasing when the radius is 5 cm?
4cm2/min
In the Book of Revelation, which of the seven churches is commended for holding fast to their faith despite being near the throne of Satan?
Pergamum