Lecture 17

Question 1

how do you find the critical points of a function?

Answer 1

1. take the derivative
2. set the derivative equal to zero
3. factors and solve for x values
4. plug the x values into the original function to create points

Question 2

how do you find the inflection points of a function?

Answer 2

1. take the first derivative
2. take the second derivative
3. set the second derivative equal to zero
4. solve for the x values in the second derivative

Question 3

how can you tell what the critical points are from a graph?

Answer 3

look where the slope is zero, where a perfect horizontal line can be drawn

Question 4

how do you find the global max’s and min’s on a closed interval?

Answer 4

1. find the derivaitve
2. set the derivative equal to zero
3. factor and solve for the x values
4. plug the critical values and the endpoints into the original function
   -the highest y value produced will be the global max and the lowest will be the global min

Question 5

is division likely to represent increasing or decreasing?

Answer 5

decreasing

Question 6

is multiplication likely to represent increasing or decreasing?

Answer 6

increasing

Question 7

how can you solve any optimization problem?

Answer 7

1. draw a diagram
2. create the wanted equation and constraint equation
3. isolate one variable and plug the answer into the other equation
4. find the derivative of the function created
5. isolate and solve for a variable
6. use the value of the variable and an equation to solve for the other variable