Answer: The function f(x)= -2x+3 is decreasing while the function f(x)=2x is increasing. The y-intercept for f(x)= -2x+3 is at 3, while the y-intercept for f(x)=2x is at 0.
Step-by-step explanation:
A because x+10x is 11x and 2-4 is -2
Answer:
1. C
2. A
3. C
4. C
5. I think it’s A bit I’m not sure
6. I’m sorry I don’t understand the handwriting can’t tell if that’s a fraction or an exponent
7. C
8. D
9. C
Hope this helps :)
Step-by-step explanation:
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:
651>7.904
Step-by-step explanation:
651 is greater than 7.904
