Lecture 11 Flashcards

existence of derivatives

1
Q

when do derivatives exist?

A

for a smooth graph with no sharp corners, cusps, or vertical tangents

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

what is the formula to find the derivative for the power rule?
what do the variables represent?

A

x^(p)–>px^(p-1)
p is a number

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

what is the formula to find the derivative of exponentials?

A

a^(x)–> a^(x) ln(a)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

what does it mean if two variables are inversely proportional to one another in terms of increasing and decreasing?

A

the increase in one causes a decrease in the other

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

what is the general formula to find the chain rule?

A

f ‘ [g(x)] g ‘ (x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

how can you tell if a function is an underestimate?

A

if a function is concave up, then the tangent line will lie below the curve. Hence the tangent line of approximation will be an underestimate

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

how can you tell if a function is an overestimate?

A

if a function is concave down, then the tangent line will lie above the curve. Hence the tangent line of approximation will be an overestimate

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

what does it mean if the first derivative is positive?

A

the function is increasing

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

how can you tell if a derivative is negative on a graph?

A

the slope is going from uphill to downhill

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

how can you tell if a derivative is positive on a graph?

A

the slope is going from downhill to uphill

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

if you have two negative slopes, how can you tell which one is smaller?

A

the stepper negative slope is the smaller slope

How well did you know this?
1
Not at all
2
3
4
5
Perfectly