Me with this question, it's really frustrating me.

Consider the attached figure. The coordinates of the points are

Since f(x) is even, we have

So, the updated coordinates are

This implies that the rectangle has area

And we want to maximize this function. To so do, let's compute its derivative:

This equals 0 if

Given the behaviour of the area function (cubic polynomial with negative leading coefficient), the first point is a minimum, and the second point is a maximum. So, for x=2, we have

Which yields an area of

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

congruent segments

step-by-step explanation: