2.5,2.6,3.9 Test Flashcards
When should implicit differentiation be used?
If you cannot easily, if at all, solve for y.
What is implicit differentiation?
When you solve for dy/ dx
How do you use implicit differentiation?
Whenever you find the DERIVATIVE of something with a y, you put a dy/dx after it. Then solve for dy/dx.
What is the relation to dy/dx with a horizontal tangent line?
Dy over dx= 0
MEANING dy=0 and dx CANNOT equal 0
What is the relation to dy/dx with a vertical tangent line?
dx=0 and dy CANNOT equal 0
How do you find the second plus derivatives with implicit differentiation?
You find the second derivative like normal but you might have to plug in the first derivative at times
What is important to remember with implicit differentiation?
DO NOT FORGET PRODUCT RULE AND QUOTIENT AND CHAIN RULE AND STUFF
Derivative of sin x
Cos x
Derivative of cos x
negative Sin x
Derivative of tan x
Sec ^2 x
Derivative of cot x
- csc^2 x
Derivative of csc x
negative (csc x) (cot x)
Derivative of sec x
(sec x) (tan x)
What do you call a problem that has a 0 in the denominator?
Undefined
How do you find the slope of a tangent line to a graph using implicit differentiation?
Find the derivative using implicit differentiation, then plug the point into the derivative to find the slope
How do you find the equation of a tangent line to a graph using implicit differentiation?
Find the derivative using implicit differentiation, then plug the point into the derivative to find the slope. Then, plug the point into a y=mx+b equation to find the b value.
How do you find the points when the graph of the equation has a horizontal or vertical tangent line?
First find the derivative of the function. Then, clump the x’s and y’s together. For the horizontal line use the y’s. Set the y equation to 0, then find the zeroes of y and those will be your two y values for your two points and the x values will be whatever x equals when you set the numerator equal to 0. Then do the same for the vertical line with the denominator.
How do you solve a related rate problem?
Translate- Figure out what you are solving for
Relate variables- write down all variables and the equation you will be finding the derivative of
Relate the rates and answer question- now solve by plugging things in and solving for what you said in step 1
Area of a circle
pi r squared
Circumference of a circle
2 pi r
Area of a triangle
1/2 base times height
Volume of a sphere
4/3 pi r cubed
What is an important thing to remember with related rates?
PUT DOWN THE CORRECT UNITS
Volume of a cone
1/3 pi r squared h
How do you decide which trig function to use in related rates working with similar triangles?
Use the one that uses the information that was directly given to you, SPECIFICALLY THE DERIVATIVE
Practice #3,5,7 related rates worksheet
Practice #18,25b,41 on 2.6 PS B
Surface area of a cube
6a^2
a- side length
If you are asked to find the value of a limit while using the limit definition, what do you HAVE TO REMEMBER?
Do not plug in 0, leave it as is and just find the derivative of the function that is being subtracted at the end
ex: look at chapter 2 test number 17
