Implicit Differentiation
Higher Derivatives
Related Rates
100
Discuss when ID is needed
What is When a function is written in terms of x and y
100
The rate of change of the rate of change is known as what?
What is acceleration
100
Why are the problems called related rates?
What is Because in the problems, physical factors are working in concert with each other and the derivatives are related to one another based on the problem.
200
What is the radius of this circle? x^2 + y^2 = 34
What is root 34
200
What is the 27th derivative of cos(x)?
What is sin(x)
200
Using the Law of Sines on a related rate problem, what would you have to be careful of in terms of SSA
What is The Double Solution Case for SSA
300
True/False: Implicit Differentiation can be mixed with the Chain Rule.
What is True
300
Player Challenge
What is Find the jerk of f(x) = 2x^3
300
Why do we need to use proportions on some related rate problems?
What is Because to take the derivative of a function, you can only have one independent variable.
400
Player Challenge:
What is Differentiation: 1/x + 1/y = 1
400
Explain how to tell if a particle is moving backwards in terms of derivatives.
What is A particle moves backwards if the particles velocity and acceleration have opposite signs.
400
Explain why you do not plug in given information before te derivative is taken.
What is Because in these problems, the given information is only valid for "rates". Plugging the information in too early would not make sense because you are solving for some kind of related rate. It would be compared to, "putting the cart before the horse".
500
If you were told to solve for dx/dy, find the derivative of the following: x^2 + y^2 = 31
What is Answer on board
500
If a(t) < 0 and v(t) < 0, explain the motion of the particle.
What is Forward
500
In a related rate problem, if we have variables such as volume and height, why do we have to use the chain rule on each variable?
What is Because they are both functions of time.
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