Because we will have to do it eventually, let's find f(x) first.
f''(x) = 24x - 18
First, we integrate f''(x) using an indefinite integral.
f'(x) = ∫ (24x - 18) dx
f'(x) = 12X^2 - 18x + C
Now, we need to find C by substituting "x" for -1 and setting the equation equal to -6 because f'(-1) = -6
f'(-1) = 12(-1)^2 - 18(-1) + C = -6
Solve for C
C=-26
Now we put that into f'(x).
f'(x) = 12x^2 - 18x -26
Now, we integrate again.
f(x) = ∫(12x^2 - 18x - 26)dx
f(x) = 4x^3 - 9x^2 - 26x + C
Now, we substitute "x" for 2 and set it equal to 0.
f(2) = 4(2)^3 - 9(2)^2 - 26(2) + C = 0
Solve for C
C=38
Now that we have f(x), B has been solved.
Next, we need to find out where the slope of f(x) is equal to 0. Remember that to find slope, we need to find the derivative. We already found the derivative of f(x), so we can use that. The question asks for the places where the slope of f(x) is 0, so we need to set f'(x) equal to 0 and solve for "x"
12x^2 - 18x -26 = 0
I could try to factor this, but I know that it is not possible. We must use the quadratic formula. I cannot reasonable put the quadratic formula into this, so I will only do the part under the radical.
√[18^2-4(12)(-26)]
√(324+1248)
√1572
√(4)*√(393)
2√393
When this is done with the rest of the formula, you get.
[18+/-2√(393)]/24
Thus, the points where the slope of f(x) is equal to zero are where <span>[18+/-2√(393)]/24 are the x values of f(x).
( </span>[18+/-2√(393)]/24 , f ( <span>[18+/-2√(393)]/24 ) )
Now, we have done A and B.
To do C, we must remember the formula for finding the average value of f(x)
This formula is:
[The </span>definite integral of f(x)] / (b-a)
The picture is of this formula.
When we solve for this, we get -13.
I hope I got everything right.
Answer:
may both is the correct answer
Answer:
Step-by-step explanation:
The length of arc RS is given by:
From the diagram the radius is 
and the central angle of sector RS is 
We use 
and substitute the radius and central angle to obtain:
We simplify to get:
Answer:
width of the border is 3 inches
Step-by-step explanation:
Given data
size = 8 inches by 10 inches
area = 144 square inches
to find out
width of the border
solution
first we consider width of border is x
area of new full rectangle = (8 + 2x ) × ( 10 + 2x )
so we know area of photo = 8 × 10 = 80 square inches
and area of border = 144 square inches that is given
so new area of photo with the border is 80 + 144 = 224 square inches
and we can say that
area of full rectangle - area of the photograph = Area of Border
(8 + 2x) × (10 + 2x) – (80) = 144 square inches
80 + 16x + 20x + 
– 80 = 144
+ 36x – 144 = 0
solve thios equation we get
+ 9x – 36 = 0
solve thios equation we get
(x + 12) (x – 3) = 0
so here x have two value one is negative and other is positive
so we consider only positive value
x = -12 or x = 3
width of the border is 3 inches
Answer:
r
Step-by-step explanation:
