O, L, and E

Question 1

Locally Linear Function

Answer 1

If you zoom in on a point in a function, the curve will look like a straight line.

Question 2

Not locally Linear function

Answer 2

If you zoom in on a point in a function, the curve never looks like a straight line

Question 3

Which point on the graph of y=… is closest to the point (x,y)?

Answer 3

Use distance formula and square it
x1 = x
Differentiate and set equal to zero
Plug x into the original equation

Question 4

Distance Formula

Answer 4

d=√((x2-x1)²+(y2-y1)²)

Question 9

What is the volume formula for a cube

Answer 9

x²h

Question 10

Steps to solve for least amount of surface area given volume

Answer 10

V= x²h
Solve for h
Find surface area
S=x²+4xh
Plug in h
Find Derivative
Set equal to 0
Solve for x
Find h

Question 11

Surface Area formula of a cube

Answer 11

S= x²+4xh

Question 12

Finding Dimensions with borders least

Answer 12

Find area
xy= A
Solve for y
Double each border and Add width to x and height to y
plug in for area
plug in y
Find derivative
Solve for 0
Find y
Plug into equation with borders

Question 13

Area of a rectangle

Answer 13

xy

Question 14

Rectangle inscribed in a parabola; maximize the area

Answer 14

Find area
A=2x*y
Simplify
Take the derivative
Set equal to zero
Solve for x
Plug into original equation for y
Find dimensions

Question 15

Width Rectangle on the axis

Answer 15

2x

Question 16

Problem; Find linearization of an equation with x=a

Answer 16

Plug a into f(x)
Take the derivative of f(x)
Plug in a to f’(x)
Plug derivative of f’(x) into f(a)

Question 17

Formula for linearization of f at x=a

Answer 17

L(x)= f(a)+ f’(a)(x-a)

Question 18

Use linearization for the value of f(x) at

Answer 18

Find a simple value that is close to the given
(2.01-> 2)
Plug into equation= f(a)
Find derivative
Plug into derivative equation f’(a)
Plug into f(a) +f’(a) * (x-simple value)
Plug in original value for x and subtract from simple value
Simplify

Question 19

Find the differential dy

Answer 19

Find y
Differentiate y with respect to x
Multiply by dx

Question 20

Find dy and evaluate

Answer 20

Same thing just plug in given numbers

Question 21

Actual Change

Answer 21

Write the function
y=f(x)
Plug in original and original plus change into function and subtract

Question 22

Approximate

Answer 22

Find derivative of function
Plug in given value
Multiply by change