2.5,2.6,3.9 Test

Question 1

When should implicit differentiation be used?

Answer 1

If you cannot easily, if at all, solve for y.

Question 2

What is implicit differentiation?

Answer 2

When you solve for dy/ dx

Question 3

How do you use implicit differentiation?

Answer 3

Whenever you find the DERIVATIVE of something with a y, you put a dy/dx after it. Then solve for dy/dx.

Question 4

What is the relation to dy/dx with a horizontal tangent line?

Answer 4

Dy over dx= 0
MEANING dy=0 and dx CANNOT equal 0

Question 5

What is the relation to dy/dx with a vertical tangent line?

Answer 5

dx=0 and dy CANNOT equal 0

Question 6

How do you find the second plus derivatives with implicit differentiation?

Answer 6

You find the second derivative like normal but you might have to plug in the first derivative at times

Question 7

What is important to remember with implicit differentiation?

Answer 7

DO NOT FORGET PRODUCT RULE AND QUOTIENT AND CHAIN RULE AND STUFF

Question 8

Derivative of sin x

Answer 8

Cos x

Question 9

Derivative of cos x

Answer 9

negative Sin x

Question 10

Derivative of tan x

Answer 10

Sec ^2 x

Question 11

Derivative of cot x

Answer 11

• csc^2 x

Question 12

Derivative of csc x

Answer 12

negative (csc x) (cot x)

Question 13

Derivative of sec x

Answer 13

(sec x) (tan x)

Question 14

What do you call a problem that has a 0 in the denominator?

Answer 14

Undefined

Question 15

How do you find the slope of a tangent line to a graph using implicit differentiation?

Answer 15

Find the derivative using implicit differentiation, then plug the point into the derivative to find the slope

Question 16

How do you find the equation of a tangent line to a graph using implicit differentiation?

Answer 16

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.

Question 17

How do you find the points when the graph of the equation has a horizontal or vertical tangent line?

Answer 17

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.

Question 18

How do you solve a related rate problem?

Answer 18

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

Question 19

Area of a circle

Answer 19

pi r squared

Question 20

Circumference of a circle

Answer 20

2 pi r

Question 21

Area of a triangle

Answer 21

1/2 base times height

Question 22

Volume of a sphere

Answer 22

4/3 pi r cubed

Question 23

What is an important thing to remember with related rates?

Answer 23

PUT DOWN THE CORRECT UNITS

Question 24

Volume of a cone

Answer 24

1/3 pi r squared h

Question 25

How do you decide which trig function to use in related rates working with similar triangles?

Answer 25

Use the one that uses the information that was directly given to you, SPECIFICALLY THE DERIVATIVE

Question 26

Practice #3,5,7 related rates worksheet Practice #18,25b,41 on 2.6 PS B

Question 27

Surface area of a cube

Answer 27

6a^2 a- side length

Question 28

If you are asked to find the value of a limit while using the limit definition, what do you HAVE TO REMEMBER?

Answer 28

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