Consider the function f (x) = x³ – 7x² + 3x + 2. 1) Find the derivative, f ’(x). 2) Find the second derivative, f ’’(x). 3) Find the critical numbers of f (x) - just the x-values. 4) Use either the First Derivative Test or the Second Derivative Test to determine if these critical values are a relative maximum or relative minimum. 5) Compute the corresponding y-values and clearly label the relative maximum point and relative minimum point. 6) Find the absolute maximum point and absolute minimum point of f (x) on the interval [-2, 6]. 7) Find the inflection point of f (x).
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2) To find the second derivative, f''(x), we can differentiate f'(x). Taking the derivative of each term in f'(x), we get f''(x) = 6x - 14.
3) To find the critical numbers of f(x), we set f'(x) equal to zero and solve for x. So, 3x^2 - 14x + 3 = 0. Solving this quadratic equation, we find the critical numbers x = 1 and x = 1/3.
4) To determine if these critical values are a relative maximum or relative minimum, we can use the Second Derivative Test. Evaluating f''(x) at x = 1 and x = 1/3, we find that f''(1) = -8 and f''(1/3) = -4. Since f''(1) is negative and f''(1/3) is also negative, we can conclude that both x = 1 and x = 1/3 correspond to relative maximum points.
5) To compute the corresponding y-values, we substitute the critical numbers into the original function f(x). We find that f(1) = -1 and f(1/3) = 1/27. Therefore, the relative maximum point is (1, -1) and the other relative maximum point is (1/3, 1/27).
6) To find the absolute maximum and minimum points of f(x) on the interval [-2, 6], we evaluate f(x) at the critical numbers and the endpoints of the interval. We find that f(-2) = 36, f(6) = 218, f(1) = -1, and f(1/3) = 1/27. Therefore, the absolute maximum point is (6, 218) and the absolute minimum point is (1, -1).
7) To find the inflection point of f(x), we need to find where the concavity changes. This occurs when f''(x) = 0 or is undefined. However, in this case, f''(x) is always defined and never equals zero. Therefore, there are no inflection points in the given
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Express on simplest form in terms of i: sqrt-16
4.5.11Mohamed wrote the paragraph proof to show that ADEG AEFG. What mistake did he make?ADEG and AEFG are right triangles.The figure shows DE = EF, ANDEG EG by the Reflexive Property.Therefore, by the HL theorem,ADEG AEFGGX ХChoose the correct answer below.O A. The two triangles are congruent by SAS, not the HL Theorem.O B. In AEFG, EF is a leg and in ADEG, DE is the hypotenuse, so they cannot be corresponding sides.O C. The two triangles are congruent by SSS, not the HL Theorem.OD. In AEFG, EG is a leg, and in ADEG, EG is the hypotenuse, so they cannot be corresponding sides.
An igloo has a circular floor with a radius of 2 yards. What is the floor’s diameter?
Round each number to the nearest tenth. What is the best estimate for the difference of 483.51 – 246.17? A. 230 B. 237.3 C. 237.4 D. 238
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x+7x-3-1+4
8x-4+4
8x
:)
1) Gather like terms
(x+7x)−1+4−3
2) Simplify
8x−1+4−3
3) Simplify
8x
B.$5607.42
C.$4846.84
D.$22,429.68
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You would get this by adding $13,638.26 + $8,791.42 = $22,429.68.
The correct answer is D.
Answer:
Angelica's gross income from the two jobs last year is $22,429.68
Step-by-step explanation:
Angelica had two jobs last year, and she received two W-2 forms.
On the first W-2 form, the figure in box 1 was $13,638.26,
while on the second W-2 form, the figure in box 1 was $8791.42.
Income from first job is $13,638.26
Income from second job is $8791.42
Total income = first job income + second job income
=13638.26 + 8791.42 = 22,429.68
Angelica's gross income from the two jobs last year is $22,429.68
Answers
Answer:
0.0425
Step-by-step explanation:
probability of basket player = 0.25
probability of being a soccer player = 0.17
chances that a sixth grader plays basketball AND soccer = 0.25×0.17 = 0.0425
Answers
=> First let’s add the total amount of hours Theresa rendered.
=> 9 + 7 = 16 hours in total
Her total pay was $116.00. What is her rate per hour?
=> Let’s solve for the unit rate:
=> 16 hours for 116 dollars.
Let’s find x dollars / hour
=> 116 dollars / 16 hours = 7.25 dollars / hour.
Thus, she is paid 7.25 dollars every hour she do her work
9 hours on Monday + 7 hours on Wednesday = 9 + 7 = 16 hours
$116.00 / 16 hours = 116.00 / 16 = $7.25
The correct result would be $7.25.
Answers
Answers
Usually, you get the m and b
the b is the y-intercept. (where the line meets on the y-axis)
the m is the slope of the line.
So now how you use it.
Basically, if I ask you to graph the line y=2x+5
When you graph the line look at the b (y=2x+5) . Remember: The b is the y-intercept.
Then you're going to make your first point (0,5)
Then you have to do the slope of the line y=2x+5
Remember slope is Rise/Run. So the slope is 2/1.
So make the slope 2. If you did this correctly your line should cross through the point (7,1)
Hope this helps! If you still don't understand then ask your teacher for more help!