Lecture 14

Question 1

what is the derivaitive of tan?

Answer 1

sec^(2)(x)

Question 2

why is it impossible to express a circle as a single equation?

Answer 2

because each x value produces two y values

Question 3

why does the expression for the derivative at a point must depend on both x and y on a circle?

Answer 3

because the equation is in terms of both x and y

Question 4

what are the steps to differentiate implicitly?

Answer 4

1. write d/dx on both sides of the equation
2. find the derivative of both sides of the equation
3. collect like terms on each side
4. factor out y’
5. isolate for y’

Question 5

how do you find the horizontal tangent on an implicit function?

Answer 5

1. find the derivative
2. set the derivative equal to zero
3. solve for the x value(s)

Question 6

how do you find the verticle tangent on an implicit function?

Answer 6

1. find the derivative
2. set the denominator of the derivative equal to zero
3. solve for the y value

Question 7

how do you estimate the y value given and the x value and an implicit function?

Answer 7

1. find the derivative of the implicit function
2. plug the x value into the derivative to find the slope
3. plug the x value into the original function to create a point
4. use the slope, point and linearization formula to create the approximation equation
5. plug in the x value of interest into the approximation equation to get the answer