CPhill

I think I've got it

Son

Son's Father 

Son's Grandfather

If even....then  f(x)  = f(-x)

So   f(-x)  =  2(-x)^3 - (-x)^2   =  -2x^3 - x^2    ...this isn't equal to  f(x)

If odd....then  -f(x)  =  f(-x)

-f(x)  =  -  [ 2 x^3  - x^2 ]  =  -2x^2 + x^2    ...and this isn't equal to f(-x)

So....neither

Increasing  on  (-inf, 0)  and (1, 2)

OK....it just shows up for me.....don't worry about it....!!!

Ok....thanks, ILP.....I didn't know if the users could do that, or not....

I think you can just hit "best answer" under my question......I don't often give myself the "best answer" because I'm never sure if someone else might not explain it better...

1.

The relative minimum of the function occurs at (1, -5) ⇒    y  = -5

(This is actually the absolute minimum, too )

2.  The function is constant  on  the interval (2, 6).....the function's value is unchanging on this interval

Note that  we know the side opposite the 20°  angle

And we're looking for the adjacent side, x

The trig function  that relates the opposite and adjacent is the tangent

So

tangent (angle measure)  = opp / adj

tangent (20° )  =  9 / x      .....multiply both sides by x

x * tan (20)  = 9             .....divide both sides by tan (20)

x  =  9  / tan (20)  = 24.72

I think you mean  ( f / g) x  =

f (x)  / g(x)  =

[ 4x^2 + 19x  - 5 ]  /  [ 4x^2 - x ]     factor numerator / denominator

Note..it you're having trouble factoring....try factoring the "easier" thing, first....this is the denominator

[ 4x^2 + 19x - 5 ]  /  [  x (4x - 1 ) ]      guess that the numerator includes 4x - 1 as a factor

[ ( 4x - 1) ( x + 5 ) ] [ x (4x - 1 ) ]

Note that the numerator factors perfectly..."cancel" the  4x - 1  on top/bottom

(x + 5 )  / x          x not equal to  0, 1/4

Good job, RP!!!

First, let's convert feet to yards

Remember  3ft  = 1 yd....so divide ft by 3 to get the yards

18 feet / 3   =  6 yds

4 inches  = 1/3 ft / 3  =  1/9  yds

So....the total volume is

(6 yds) x (6 yds )  x (1/9 yds )     =

36  x 1/9   =      4 yds^3

So....the cost is

( 4 yds^3)  x $41  per  yd^3   =   $ 164