Principles
What does the negative symbol mean for the rate of change?
What is the rate of change is decreasing?
What is the first step in solving related rates problems?
What is read the problem & draw a diagram?
What is the value that we asked to look for?
What is find?
*Draw a diagram
The width of a rectangle is increasing at a rate of 2 cm/sec and its length is increasing at a rate of 3 cm/sec. At what rate is the area of the rectangle increasing when its width is 4 cm and its length is 5 cm?
What is a rectangle with a length= 5 cm and width= 4 cm label?
What is another word for slope and/or derivative (commonly used in related rates problems)?
What is the rate of change?
What is the second step in solving a related rate problem?
What is identifying all quantities as "Known," "Given," and "Find"?
What is the value that is written in the word problem and that we plug in?
What is the given?
*Identify "Known", "Given", and "Find"
The width of a rectangle is increasing at a rate of 2 cm/sec and its length is increasing at a rate of 3 cm/sec. At what rate is the area of the rectangle increasing when its width is 4 cm and its length is 5 cm?
What is..
Known: A= LW
Given: L= 5 cm and W= 4 cm
Find: dA/dt when dL/dt = 3 cm/sec and dW/dt= 2 cm/sec
What is the rule that takes the derivative of the outer function and multiplies it by the derivative of the inner function?
What is the chain rule
What is the third step in solving a related rate problem?
What is writing an equation that relates the variables?
What is the value that we get from drawing a diagram?
What is the known/equation?
*Use chain rule to implicitly differentiate both sides
The width of a rectangle is increasing at a rate of 2 cm/sec and its length is increasing at a rate of 3 cm/sec. At what rate is the area of the rectangle increasing when its width is 4 cm and its length is 5 cm?
What is
dA/dt=L(dW/dt) + W(dL/dt)
What is the term that means to take the derivative with respect to time, t?
What is implicit differentiation?
What is the fourth step in solving a related rate problem?
What is using the chain rule to implicitly differentiate both sides of the equation with respect to time, t?
What is the value that we need to get by itself on one side?
What is the rate of change?
*Plug in both sides to solve
The width of a rectangle is increasing at a rate of 2 cm/sec and its length is increasing at a rate of 3 cm/sec. At what rate is the area of the rectangle increasing when its width is 4 cm and its length is 5 cm?
What is
dA/dt = (5)(2)+(4)(3)
dA/dt = 10+12
dA/dt= 22 cm^2/sec
What is the final step in solving a related rate problem?
What is plugging in the known values and solving for the unknown?