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Oksi-84 [34.3K]
2 years ago
15

OMG CAN SOMEONE PLEASE ANSWER MY QUESTIONSS LIKE THIS IS SO IMPORTANT AND YALL REALLY DONT CARE CAN YALL PLEASE GO TO MY THING A

ND ANSWER SOME MATH ONES I JUST POSTED PLEASEEEE I REALLY NEED HELP AND LITERALLY NO ONE HELPS ME NO WHERE AT ALL
Mathematics
1 answer:
Aleks04 [339]2 years ago
4 0
You didn’t put the math problems for us to answer the questions
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F(x) = x2 − x − ln(x) (a) find the interval on which f is increasing. (enter your answer using interval notation.) find the inte
Mekhanik [1.2K]

Answer:

(a) Decreasing on (0, 1) and increasing on (1, ∞)

(b) Local minimum at (1, 0)

(c) No inflection point; concave up on (0, ∞)

Step-by-step explanation:

ƒ(x) = x² - x – lnx

(a) Intervals in which ƒ(x) is increasing and decreasing.

Step 1. Find the zeros of the first derivative of the function

ƒ'(x) = 2x – 1 - 1/x = 0

           2x² - x  -1 = 0

     ( x - 1) (2x + 1) = 0

         x = 1 or x = -½

We reject the negative root, because the argument of lnx cannot be negative.

There is one zero at (1, 0). This is your critical point.

Step 2. Apply the first derivative test.

Test all intervals to the left and to the right of the critical value to determine if the derivative is positive or negative.

(1) x = ½

ƒ'(½) = 2(½) - 1 - 1/(½) = 1 - 1 - 2 = -1

ƒ'(x) < 0 so the function is decreasing on (0, 1).

(2) x = 2

ƒ'(0) = 2(2) -1 – 1/2 = 4 - 1 – ½  = ⁵/₂

ƒ'(x) > 0 so the function is increasing on (1, ∞).

(b) Local extremum

ƒ(x) is decreasing when x < 1 and increasing when x >1.

Thus, (1, 0) is a local minimum, and ƒ(x) = 0 when x = 1.

(c) Inflection point

(1) Set the second derivative equal to zero

ƒ''(x) = 2 + 2/x² = 0

             x² + 2 = 0

                   x² = -2

There is no inflection point.

(2). Concavity

Apply the second derivative test on either side of the extremum.

\begin{array}{lccc}\text{Test} & x < 1 & x = 1 & x > 1\\\text{Sign of f''} & + & 0 & +\\\text{Concavity} & \text{up} & &\text{up}\\\end{array}

The function is concave up on (0, ∞).

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3 years ago
Write 12.4% as a decimal and simplified fraction
Gnom [1K]

Given the following question:

We are given 12.4%

undefined

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1 year ago
What is an equation of the line that passes through the points (5,8) and (-5,2)?
deff fn [24]

hi there! here's my answer for you...

Answer:

y = 3/5x + 5

Explanation:

Use the slope formula and slope-intercept form y = mx + b to find the equation.

<em>hope this helped. have a good one!</em>

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Fraction=8/20 kids ate a grilled cheese at her restaurant in the last week. This simplifies to 2/5. Therefore the probability that a randomly selected child at her restaurant is eating a grilled cheese is 2/5.
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Answer:

B. slope

Step-by-step explanation:

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