Unit 6

Question 1

How do you find absolute extrema?

Answer 1

1. Find all critical points on the interval
2. Evaluate the function values at all the critical points and the end points
3. Compare all function values and pick the largest and smallest for absolute max and min

Question 2

What does the critical point theorem state?

Answer 2

States that if a function has one critical point on the interval, if that point is a relative max it is the absolute max and if it is a relative min it is the absolute min

Question 3

How do you solve an application of extrema question?

Answer 3

1. Read careful!!
2. Draw diagram!
3. Decide what variable must be minimized or maximized, then express it as a function of one other variable
4. Find the domain of the function
5. Find the critical points of that function
6. Find the values of the critical numbers and endpoints or limits of endpoints to find absolute extrema

Question 4

How do you make an open box from a square piece of paper?

Answer 4

Cut four identical squares out of each corner and fold the flaps up

Question 5

What does dy/dx mean in words?

Answer 5

Means we differentiate an expression in y with respect to x

Question 6

How do you implicitly differentiate?

Answer 6

You differentiate every term and variable except when you differentiate x you add a “dx/dx” to it and when you differentiate y you add a “dy/dx” then you get all dy/dx to one side and solve for dy/dx to get derivative

Question 7

How do we solve related rates questions?

Answer 7

They are differentiating with respect to time (dy/dt)
First draw a diagram of the situation
Then write an equation relating the variables (Pythagoras theorem)
Then use implicit differentiation to find derivative of both sides of equation
Then solve for the derivative (slope) you need

Question 8

What is the equation of similar triangles?

Answer 8

a/c = (a+b)/c

Small triangle is c on bottom then a on sides
Bigger triangle extended from small triangle has b extended from a and d on the bottom as a base
a
a a
a c a
b b
b d b

Question 9

How do we linear approximate?

Answer 9

f(x1)~f(x0) + f’(x0)(x1-x0)
x1= desired number that’s hard to get from calculator
f(x1)= given equation that’s hard to calculate
f(x0)= number that when plugged into equation gives an exact number and is close to x1
f’(x0) is where you derive the equation in the given function and plug your easy number in so say you’re given root23 you’d derive rootx and plug 25 in

Question 10

What is the alternate form of linear approximation involving Δy?

Answer 10

Δy~dy/dx (Δx)