Motion
The derivative of position
Velocity
The first step for related rates
Write an equation relating the identified variables
What form is used for tangent lines
Point slope form
The derivative of velocity
Acceleration
How do you differentiate during a related rates problem
Differentiate with respect to time/implicit differentiation
What is the slope of a line tangent to a point c along a function f
f'(c)
If the velocity of a car is modeled by v(t) = 4t2-7t-11 and measured in m/s, what is the speed of the car at t=2s.
9 m/s?
What is a side quest in the context of related rates
Solving for an unknown variable in terms of another unknown variable
If f(x) = 3x2-2x approximate f(1.9) using the line tangent to f(2)
f(1.9) = 7
If the position of a car is modeled by x(t) = -2t3+t2-8t+3 and measured in m, what is the acceleration of the car at t = 3s.
-34m/s2?
The volume of a sphere is increasing at a rate of 3 cm3/min. What is the rate that the diameter is increasing when the when the radius is 15 cm
1/150pi cm/min
If f(x) = (3x)1/2 approximate the value of f(4.1) using the line tangent to f(4)
f(4.1) = ((3)1/2/40)+2(3)1/2