What are the coordinates of the turning point for the function f(x) = (x+3)^3 + 1

The turning points for the given function is (-3,1).

Step-by-step explanation:

The given function is

The turning point of a function where the .

Equate the first derivative equals to 0.

At the turning point the x-coordinate is -3.

Substitute x=-3 in the given function.

At the turning point the y-coordinate is 1.

Therefore the turning point is (-3,1).

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet