Chapter 4 Test

Question 1

Product Rule Formula

Answer 1

d/dx[f(x)g(x)] = f(x)d/dx[g(x)] + g(x)*d/dx[f(x)]

Question 2

Quotient Rule Formula

Answer 2

d/dx[f(x)/g(x)] = {g(x)d/dx[f(x)] - f(x)d/dx[g(x)]}/[g(x)]^2

Question 3

Steps to finding absolute max and min

Answer 3

1. Find f’(x)
2. Find C.N’s (set f’(x) equal to 0) *If domain error, set denominator equal to 0
3. Find y values for C.N’s *If C.N’s are on open interval, skip this step
4. Find y values for interval points
5. Highest=max, Lowest=min

Question 4

Steps to finding equation of tangent line

Answer 4

1. Find f’(x)
2. Plug x value of point into f’(x) to find slope
3. Put point and slope value into point slope equation (y-y1) = m(x-x1)

Question 5

Steps to finding all the values where the tangent line of f(x) is #

Answer 5

1. Find f’(x)
2. Set f’(x) = #
3. Solve for x

Question 6

Steps for finding when the impact will happen

Answer 6

1. Set f(x) = 0

2. Solve for t

Question 7

Steps to finding the instantaneous velocity/velocity at impact

Answer 7

1. Find f’(x)

2. Plug t value (found in time of impact problem) into f’(x)

Question 8

Steps to finding total average velocity

Ex: t = 1, t = 3

Answer 8

1. [s(3) - s(1)]/(3-1) = ?

Question 9

Steps to finding the average velocity at a given point

Ex: [1,2]

Answer 9

1. [f(2) - f(1)]/(2-1)

Question 10

Steps to finding the slope of a tangent line using limit process of f(x) at (c,f(c))
Ex: f(x) = 3 - 2x, (-1,5)

Answer 10

1. {[3-2(-1+h)] - 5}/h

Question 11

f’(x) is…

f’‘(x) is…

Answer 11

f’(x) is slope/velocity

f’‘(x) is acceleration