Show:
Derivatives
Motion
EVT/MVT
Implicit Differentiation
Related Rates
100
Find the derivative: y=3/(x^3)
-9x^-4
100
The position function of an object in motion is given by x(t)=t^3+2t^2-4t+3 meters in 0≤t≤4 seconds. In this interval: Find the acceleration at 3 seconds.
22 m/s^2
100
Find the values of c that satisfy the MVT for the given function and interval. f(x)=x^2+4 on the interval [1,2]
3/2
100
Find dy/dx: x^3-y^3=y
-3x^2 / -3y^2-1
100
A rock is dropped into a pond and creates a ripple that is moving out at a rate of 5cm/sec. At what rate is the area of the circle growing when the edge of the ripple is 10 cm away from where the rock was thrown?
100pi
200
Find the derivative y=1/√(x-3)
-1/2(x-3)^(-3/2)
200
The position function of an object in motion is given by x(t)=t^3+2t^2-4t+3 meters in 0≤t≤4 seconds. In this interval: is the speed increasing or decreasing at 2 seconds?
Increasing
200
What is the absolute minimum for the function f(x)=3x^2+5x-2 on the interval [-1,1]
-4.083
200
Find dy/dx: x^4+y^4=10
-4x^3 / 4y^3
200
A 10-foot long ladder is leaning against a vertical wall. The ladder is being pushed from the bottom horizontally toward the wall at a rate of 10ft/sec. How fast is the top of the ladder being pushed up the wall when the bottom of the ladder is 6 ft from the wall?
15/2
300
Find the slope of the line tangent to the curve y=(2x+2)^(3/2)
3/2(2x+2)^(1/2)*(2)
300
The position function of an object in motion is given by x(t)=t^3+2t^2-4t+3 meters in 0≤t≤4 seconds. In this interval: when does the object stop?
2/3 seconds
300
Find the values of c that satisfy the MVT for the given function and interval. f(x)=(6/x)-5 on the interval [-3,2]
MVT Does not apply
300
Find dy/dx: y^2+2y=4x^2+2x
8x+2 / 2y+2
300
A spherical balloon is being inflated so that its volume is increasing at a rate of 36π in^3/sec. How fast is the radius of the balloon increasing when the diameter is 8 inches?
9/16
400
Find the slope of the line tangent to the curve f(x)=4x^3-2x^2+3 at the point (1,5)
8
400
The position function of an object in motion is given by x(t)=t^3+2t^2-4t+3 meters in 0≤t≤4 seconds. In this interval: What is it's displacement?
80 m
400
What is the absolute minimum for the function f(x)= x^2-4 on the interval [-3,-1]?
-3
400
Find dy/dx: x^3-5xy=3x+5y
-3x^2 +5y+3 / -5x-5
400
Oil is running into an inverted conical tank at a rate of 4π m^3/min. If the tank has a radius of 6 meters at the top and a depth of 8 meters, how fast is the depth of the oil changing when it is 4 meters?
4/9
500
Find the equation of the line tangent to the curve y=√(x^2+3x) at x=1
y-2=5/4(x-1)
500
The position function of an object in motion is given by x(t)=(4t^3)/3-10t^2+16t+2 meters in 0≤t≤5 seconds. In this interval: what is the average velocity?
-2/3 m/s
500
Find the values of c that satisfy the MVT for the given function and interval. f(x)=(6/x)-5 on the interval [-3,-1]
-2
500
Find dy/dx: sinx-cosy=y^2-x^2
-cosx-2x / siny-2y
500
Water is being poured into a conical cup that is 6 cm high and has a diameter of 6cm at the top of the cup. Right now there is a height of 5cm of water in the cup. If the water is pouring into the cup at a rate of 2 cm^3/s, what is the rate at which the height of the water is changing?
8/25π