I) If f(x) = (6x2 – 6)(7x + 6), find f'(3) using the product rule

1,308

Step-by-step explanation:

we start by differentiating the two;

Using the product rule;

F’(x) = u•v’(x) + v•u’(x)

let u = 6x^2-6

u’(x) = 12x

v = 7x + 6

v’ = 7

Substituting these, we have;

f’(x) = 7(6x^2-6) + 12x(7x + 6)

Substituting the value of 3, we have

f’(3) = 7)48) + 36(27)

f’(3) = 1,308

the answer for this question is 38

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