To solve this, you have to know that the first derivative of a function is its slope. When an interval is increasing, it has a positive slope. Thus, we are trying to solve for when the first derivative of a function is positive/negative.
f(x)=2x^3+6x^2-18x+2
f'(x)=6x^2+12x-18
f'(x)=6(x^2+2x-3)
f'(x)=6(x+3)(x-1)
So the zeroes of f'(x) are at x=1, x=-3
Because there is no multiplicity, when the function passes a zero, he y value is changing signs.
Since f'(0)=-18, intervals -3<x<1 is decreasing(because -3<0<1)
Thus, every other portion of the graph is increasing.
Therefore, you get:
Increasing: (negative infinite, -3), (1, infinite)
Decreasing:(-3,1)
That is a question about perimeter of rectangle.
The perimeter of a geometric shape is the sum of the value of the all sides.
In a rectangle, the opposite sides are cogruentes (equals). For example, look at picture below. In that rectangle, the sides AB and DC are equals, and the sides AD and BC are equals.
So, the sides of that rectangular table are: 1.52m, 1.52m, 0.75m and 0.75.
Therefore, the perimeter of that rectangle is 
m.
But that is not the final answer because that is the perimeter in meters and the question want the answer in centimeters.
1 meter has 100 centimeter, so we need to multiplicate the perimeter by 100.
Thus, the perimeter of that rectangular table is 
cm.
I believe it is A but i am not 100% sure
Circumference of a circle - derivation
This page describes how to derive the formula for the circumference of a circle.
Recall that the definition of pi (π) is the circumference c of any circle divided by its diameter d. Put as an equation, pi is defined as
π
=
c
d
Rearranging this to solve for c we get
c
=
π
d
The diameter of a circle is twice its radius, so substituting 2r for d
c
=
2
π
r
If you know the area
Recall that the area of a circle is given by
area
=
π
r
2
Solving this for r
r
2
=
a
π
So
r
=
√
a
π
The circumference c of a circle is
c
=
2
π
r
