Lecture 11

Question 1

when do derivatives exist?

Answer 1

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

Question 2

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

Answer 2

x^(p)–>px^(p-1)
p is a number

Question 3

what is the formula to find the derivative of exponentials?

Answer 3

a^(x)–> a^(x) ln(a)

Question 4

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

Answer 4

the increase in one causes a decrease in the other

Question 4

what is the general formula to find the chain rule?

Answer 4

f ‘ [g(x)] g ‘ (x)

Question 5

how can you tell if a function is an underestimate?

Answer 5

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

Question 6

how can you tell if a function is an overestimate?

Answer 6

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

Question 7

what does it mean if the first derivative is positive?

Answer 7

the function is increasing

Question 8

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

Answer 8

the slope is going from uphill to downhill

Question 9

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

Answer 9

the slope is going from downhill to uphill

Question 10

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

Answer 10

the stepper negative slope is the smaller slope