Chapter Sections 5.4-5.5 Flashcards Preview

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Flashcards in Chapter Sections 5.4-5.5 Deck (19)
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1

when considering the second derivative test:
if f ' (c) = 0 and f '' (c)

LOCAL MAX

2

when considering the second derivative test:
if f ' (c) = 0 and f '' (c) > 0 then f has local ___ at c

LOCAL MIN

3

what is the equation for the surface area of a cylinder

SA= 2( pi )( r )( h ) + 2( pi )( r^2)

4

what is the equations for the volume of a cylinder

Volume of a cylinder = ( pi )( r^2 )( h )

5

what is the distance equation?

D = Rate * Time

6

what is the equation for the surface area of a cone?

SA = ( pi )( r )( length ) + ( pi )( r^2 )
**** if it has no top then take out the "( pi )( r^2 )

7

what is the equation for the volume of a cone?

( 1/3 )( pi )( r^2 )( h )

8

what is the distance formula?

D = "square root of" (x2-x1)^2 + (y2-y1)^2

9

what is the linearization equation?

L(x) = f(a) + [f ' (a)(x-a)]

10

when finding the linearization of f(x) = (1+x)^k what is a shortcut? *when x is small values and k = any #*

L (x) = 1 + kx
*powers of 1 + x*

11

how do you make a differential equation

dy/dx = *derivative of f(x)* ..... => then just multiply both sides by dx to get => dy = *derivative of f(x)* x (dx)

12

what is the equation for absolute change and percent change in "true change"

TRUE CHANGE:
Abs Change: delta F = f ( a + dx ) - f ( a )
Percent Change: [(delta F)/ f ( a ) ] x 100

13

What is the equation for absolute change and percent change in "estimated change"

ESTIMATED CHANGE:
Abs Change: df = f ' ( a ) x (dx)
Percent Change: [ (df)/ (f (a))] x 100

14

what is the equation of the surface area of a rectangular prism?

A=2(wl+hl+hw)

15

what is the equation of the surface area of a sphere?

A=4πr^2

16

what is the equation of the volume of a sphere?

V=(4/3)πr^3

17

what is the equation of the area of a circle?

A= (pi)(r^2)

18

what is the equation of the circumference of a circle?

either
A= 2 (pi) (r)
or
A = Diameter * (pi)

19

what is the equation of the area of an equilateral triangle?

A=("root" 3/4)a^2
a = the length of the sides which should all be equal because it is an equilateral triangle