Chapter Sections 5.4-5.5 Flashcards
when considering the second derivative test:
if f ‘ (c) = 0 and f ‘’ (c)
LOCAL MAX
when considering the second derivative test:
if f ‘ (c) = 0 and f ‘’ (c) > 0 then f has local ___ at c
LOCAL MIN
what is the equation for the surface area of a cylinder
SA= 2( pi )( r )( h ) + 2( pi )( r^2)
what is the equations for the volume of a cylinder
Volume of a cylinder = ( pi )( r^2 )( h )
what is the distance equation?
D = Rate * Time
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 )
what is the equation for the volume of a cone?
( 1/3 )( pi )( r^2 )( h )
what is the distance formula?
D = “square root of” (x2-x1)^2 + (y2-y1)^2
what is the linearization equation?
L(x) = f(a) + [f ‘ (a)(x-a)]
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
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)
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
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
what is the equation of the surface area of a rectangular prism?
A=2(wl+hl+hw)
what is the equation of the surface area of a sphere?
A=4πr^2
