Chapter 3 Test

Question 1

How do you find the velocity of something at time t?

Answer 1

Take the derivative of the original equation.

Question 2

How do you find out when something comes to rest?

Answer 2

Set the velocity equation equal to 0.

Question 3

How do you find the acceleration at time t?

Answer 3

Take the derivative of the velocity equation, or the derivative of the original equation twice.

Question 4

How do you figure out when an object reaches it’s maximum height?

Answer 4

Set the velocity equation equal to 0.

Question 5

How do you figure out what an object’s maximum height is?

Answer 5

Plug in the answer from the max height equation (in t) into the original equation.

Question 6

What is the quadratic formula?

Answer 6

negative b plus or minus the square root of b squared minus 4 a times c divided by 2 a

Question 7

How do you figure out when an object hits the ground?

Answer 7

Set the original equation equal to 0

Question 8

How do you find the velocity of an object when it his the ground?

Answer 8

Plug in WHEN it hits the ground to the velocity equation.

Question 9

How do you figure out how fast something is growing?

Answer 9

Get the derivative of the entire word problem. Even what’s before the equal sign.

Question 10

If a variable is not present in an equation, what rule should be used?

Answer 10

Constant Rule (don’t take a derivative, just leave as is)

Question 11

What is the equation used with the ladder word problem?

Answer 11

A^2 + B^2 = C^2

Question 12

Why can’t you plug in A B and C when taking the derivative of the ladder equation?

Answer 12

Because all of the numbers will then be constants which will make all the numbers 0

Question 13

What is the equation for the area of a circle?

Answer 13

A = pi R squared

Question 14

Sum Rule

Answer 14

d/dx (f(x) + g(x)) = d/dx f(x) + d/dx g(x)

Question 15

Difference Rule

Answer 15

d/dx (f(x) - g(x)) = d/dx f(x) - d/dx g(x)

Question 16

Constant Multiple Rule

Answer 16

d/dx (c f(x)) = c d/dx f(x)

Question 17

Constant Rule

Answer 17

d/dx (k) = 0

k is a constant

Question 18

Power Rule

Answer 18

d/dx x^n = nx^n-1

Question 19

What is the derivative of x with respect to x?

Answer 19

1

Question 20

Exponential Rule

Answer 20

d/dx e^x = e^x

Question 21

Product Rule

Answer 21

d/dx (fg) = f dg/dx + g df/dx

Question 22

Quotient Rule

Answer 22

d/dx (f/g) = (g df/dx - f dg/dx) / (g^2)

Low Di High minus High Di Low

Question 23

d/dx sinx

Answer 23

cosx

Question 24

d/dx cosx

Answer 24

-sinx

Question 25

d/dx tanx

Answer 25

sec^2x

Question 26

d/dx cotx

Answer 26

-csc^2x

Question 27

d/dx secx

Answer 27

secxtanx

Question 28

d/dx cscx

Answer 28

-cscxcotx

Question 29

Chain Rule

Answer 29

d/dx [f(x)]^n = n [f(x)] ^n-1 d/dx f(x)

derivative of outer x derivative of inner

Question 30

How do you find the equation of the tangent line?

Answer 30

1. Plug in x to find y OR y to find x
2. Take the derivative of the function to find the slope equation
3. Plug in x to the slope equation to get the exact value of the slope
4. Plug all numbers in to find b
5. Rewrite equation correctly

Question 31

How do you find average velocity?

Answer 31

Average Velocity = Rise / Run

f(y) - f(x) / y - x

Question 32

Log Rule

Answer 32

d/dx lnx = 1/x

d/dx = ln(f(x)) = 1/f(x) * d/dx f(x) * f’(x)/f(x)

Question 33

ln(ab)

Answer 33

lna + lnb

Question 34

ln(a/b)

Answer 34

lna - lnb

Question 35

What do you do when trying to find implicit differentiation?

Answer 35

Take the derivative of both sides of the equal sign

Question 36

What rule must be used if ln is outside of a function?

Answer 36

Log Rule

Question 37

What rule must be used if ln is inside of a function?

Answer 37

Chain Rule

Question 38

How do you find the linear approximation?

Answer 38

1. Find the equation of the tangent line

2. Set equation approximately equal to equation of tangent line