Test 2: Part 1 Introduction to derivatives

Question 1

What is the definition of derivative (equation)?

Answer 1

f’(a)= lim h–> 0 f(a+h)- f(a) / h
(Part 1)

Question 2

What is the equation of the tangent line equation?

Answer 2

y - f(a) = f’(a) (x -a)
(Part 1)

Question 3

What is the geometric meaning of a derivative?

Answer 3

It is the slope of the tangent line to the graph of a function at a given point.
(Part 1)

Question 4

How do you find the critical points of a graph?

Answer 4

by setting the derivative to 0.
(Part 1)

Question 5

if a function is increasing, the derivative is _______

Answer 5

positive
(Part 1)

Question 6

if a function is decreasing, the derivative is _________

Answer 6

negative
(Part 1)

Question 7

if a function has a local ________, its derivative changes from positive to negative

Answer 7

maximum
(Part 1)

Question 8

if a function has a local _______, its derivative changes from negative to positive

Answer 8

minimum
(Part 1)

Question 9

When is a derivative not defined?

Answer 9

1.) the function is discontinous
2.) f(a) does not exist
3.) the limits do not equal to each other
(Part 1)