Chapter 2 Test

Question 1

Tangent Line

Answer 1

Goes through 1 point

Question 2

Secant Line

Answer 2

Goes through 2 points

Question 3

When asked to find the slope of a curve what are you really looking for?

Answer 3

The slope of a line that resembles that curve when you zoom in enough

Question 4

What is the formula for the slope of a secant line?

Answer 4

The limit as x approaches 0 is f(c + deltax)- f(c) over delta x

Question 5

What is the ideal value for delta x?

Answer 5

0

Question 6

How do you graph the derivative of f by just looking at the graph of f?

Answer 6

Any curves will have a slope of 0 and everything else you follow the direction it is going in.

Ex: F is a parabola. At x=3, you are at the max of the parabola, so on f’ at x=3, it is 0, then to the right of 3 on graph f it is decreasing, so do the same on graph f’ and then to the left of graph f it is increasing so do the same on graph f’

Question 7

How do you find the slope of a tangent line using the slope of a secant?

Answer 7

The slope of a secant will always have 0 on the denominator so we have to simplify until we cannot anymore

Question 8

Differentiation

Answer 8

Process of finding the derivative of a function

Question 9

What does the limit as x approaches 0 is f(c + deltax)- f(c) over delta x tell you about a derivative?

Answer 9

If this limit exists it gives us a function whose outputs are the slopes of the original function(f)

Question 10

If a function is continuous everywhere does that mean it is differentiable everywhere?

Answer 10

NO

Question 11

What does it mean if a function is differentiable?

Answer 11

It has a derivative/slope

Question 12

How are differentiability and continuity related?

Answer 12

If f is continuous, it MAY or MAY NOT be differentiable at x=c. But if f is differentiable then f is continuous at x=c. If f is not continuous at x=c, then f’(c) doesn’t exist.

Question 13

What are times that f’ will not exist?

Answer 13

• If there is a hole at x=c. Because f is not continuous at x=c, so f’(c) cannot exist.
• If there is an asymptote at x=c. Because f is not continuous at x=c, so f’(c) cannot exist.
• If there is a jump discontinuity. Because f is not continuous at x=c, so f’(c) cannot exist.
• If there is a sharp turn at x=c.
• If there is something like a sharp turn but the lines are becoming more vertical.

Question 14

If you are asked to find the slope of a tangent line to the graph of the function at a given point how do you solve this?

Answer 14

First, find the derivative of the function. Then, plug the x value into your derivative.

Question 15

Sum and Difference Rules
Ex: x^3 + 3x^2- 3

Answer 15

Find the derivative of every term and add it all together or subtract every term

Question 16

If you are asked to find the equation of a tangent line to the graph of the function at a given point how do you solve this?

Answer 16

First find the derivative. Then plug the x value into the derivative to get the slope. Then, use y=mx+b and plug the point into the equation to get the x intercept.

Question 17

Shortcut rule for derivative of a constant function

f= 5
f=7
f’=??

Answer 17

0 ALWAYS

Question 18

What is the one trig identity we need to know?

Answer 18

sin^2x + cos^2x =1

Question 19

Power Rule
Ex: F= 3x^2
f’=?

Answer 19

X^n= nx^(n-1)
f’= 3(2x^(2-1))
f’=6x

Question 20

Constant Multiple Rule
ex: f=3x^2
f’=

Answer 20

c* f(x) = c * f’(x)
f’= 3(2x^(2-1))
f’=6x

Question 21

Derivative of sin x

Answer 21

cos x

Question 22

Derivative of cos x

Answer 22

• sin x

Question 23

If asked to find velocity, what do you do?

Answer 23

Find the derivative of the function

Question 24

If asked to find acceleration, what do you do?

Answer 24

Find the second derivative of the function

Question 25

How do you interpret derivatives? Ex: Let N(t) be the number of vehicles a particular valet parks t hours into their shift. Interpret N'(3)=7.5

Answer 25

After 3 hours have elapsed since the valet began their shift, they are parking vehicles at a rate of 7.5 cars/hr. IMPORTANT PARTS: - Cars/hr - Rate

Question 26

How do you solve this question: Determine if the function is differentiable at x=2, and the function is a piecewise.

Answer 26

You have to plug 2 into all parts of the piecewise and if they equal the same thing that means the function is continuous. So then turn each piece of the function into its derivative and plug in 2 again and if it's the same then yes it is differentiable.

Question 27

How do you determine the points where a graph of a function has a horizontal tangent line?

Answer 27

Find the derivative of the graph and then set that derivative equal to 0 and find its zeroes(prolly by factoring). IF YOU CANNOT SET THAT EQUATION EQUAL TO 0 OR FIND ANY ZEROES THEN IT HAS NO TANGENT. Then, plug those x values into the ORIGINAL FUNCTION, to get the y-value.

Question 28

Practice 65 and 67 in 2.1/2.2 PS A

Question 29

What does it mean if a question says find out when the object is at rest?

Answer 29

The object is at rest when the velocity function equals 0

Question 30

Product Rule

Answer 30

fg'+ gf'

Question 31

Quotient Rule

Answer 31

B= Bottom T=Top BT'- TB' --------------- B^2

Question 32

Derivative of tan x

Answer 32

Sec ^2 x

Question 33

Derivative of cot x

Answer 33

- csc^2 x

Question 34

Derivative of sec x

Answer 34

(sec x) (tan x)

Question 35

Derivative of csc x

Answer 35

- (csc x) (cot x)

Question 36

What is a jerk function?

Answer 36

The 3rd derivative of a function

Question 37

How do you find a higher order derivative?

Answer 37

Just do the derivative of the derivative

Question 38

What is the notation for second derivative? Third?

Answer 38

d^2y/ dx^2; d^3y/ dx^3

Question 39

Chain Rule

Answer 39

f'(g(x)) times g'(x)

Question 40

What does it mean if a question asks for the instantaneous rate of change of f'?

Answer 40

Find the derivative of F'