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.
Well, it asks that you evaluate 24 for y.
Also, notice that it says "the difference of a number and 6"
So your equation should have been
y - 6
And after evaluating
24 - 6
Then solve
24 - 6 = 18
18 should have been the answer
So no, the student's work is not correct, because the student wrote a division expression instead of a subtraction equation
Answer:
3,000 attendees
Total cost = 91,000
Step-by-step explanation:
3,000 x 25 = 75,000 3,000 x 30 = 90,000
75,000 + 16,000 = 91,000 90,000 + 1,000 = 91,000
91,000 91,000
I hope this helped :)
Answer:
yes
Step-by-step explanation:
The first one is 43/72 which can’t be simplified
The second one is 17/18
