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AfilCa [17]
3 years ago
14

F(x) = lnx/x

Mathematics
1 answer:
My name is Ann [436]3 years ago
3 0
f(x) = \frac{lnx}{x}

(a) f'(x) = \frac{d}{dx}[\frac{lnx}{x}]
Using the quotient rule:
f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}
f'(x) = \frac{1 - lnx}{x^{2}}

For maximum, f'(x) = 0;
\frac{1 - lnx}{x} = 0
lnx = 1, x = e

(b) <em>Deduce:
</em>e^{x} \geq x^{e}, x > 0
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
\frac{ln(e)}{e} \geq \frac{lnx}{x}
\frac{1}{e} \geq \frac{lnx}{x}, since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
\frac{x}{e} \geq lnx
x \geq elnx
x \geq ln(x^{e})

Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
e^{x} \geq e^{ln(x^{e}})
e^{x} \geq x^{e}, as required.
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1/5+1/7+3/21 the answer is
inessss [21]

Answer:

<h2>17/35</h2>

Step-by-step explanation:

We need to get all the fractions with a common denominator before we can solve the problem.

The only fractions that have a common multiple are 1/7 and 3/21, so we'll add these first and then add 1/5.

1/7 = 3/21

Add

\frac{3}{21} + \frac{3}{21} =\frac{6}{21}

6/21 = 30/105

1/5 = 21/105

\frac{30}{105} + \frac{21}{105} = \frac{51}{105}

Simplify

\frac{51}{105} / \frac{3}{3} =\frac{17}{35}

<h3>ANSWER: 17/35</h3>

I'm always happy to help :)

4 0
3 years ago
Guys please Help me with question number (ii) and (iii)<br> Chapter : Polynomials<br> Grade : 9
Ivanshal [37]

Answer:

Step-by-step explanation:

1. (a-b-c) (a2+b2+c2-ab-ac-bc). = (a3-b3-c3).

NOTE : this is an identity 11th identity

2. (98)3

That is 98×98×98= 941192

For example. (1)3

That is 1×1×1= 1

Or (2)3

That is 2×2×2= 8. [ 2×2=4. ]. {4× 2 = 8 )

Thank you

3 0
3 years ago
The diagram shows a circle with center C, a diameter RS, and an inscribed triangle RST.
snow_tiger [21]

Answer:

x = 26

Step-by-step explanation:

m<RTS = 4x - 14 (given)

Based on the inscribed angle theorem, the measure of the inscribed angle in a semicircle = right angle (90°)

Therefore,

4x - 14 = 90

4x - 14 + 14 = 90 + 14 (addition property of equality)

4x = 104

4x/4 = 104/4

x = 26

6 0
3 years ago
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey res
Yakvenalex [24]
The question would be:

Which is the best measure of center for first period and why?

Mean, because there are no outliers that affect the center

Median, because there is 1 outlier that affects the center

Interquartile range, because there is 1 outlier that affects the center
<span>
I think the answer would be the fourth choice "</span><span>Standard deviation, because there are no outliers that affect the center"
</span>
I hope my answer has come to your help. God bless and have a nice day ahead!
8 0
2 years ago
X + 15 = 28<br> O A. x= 13<br> O B. x = 33<br> O C. x = 43<br> O D. x = 23
Mariana [72]

Answer:

A

Step-by-step explanation:

the answer is

x+15=28

x=28-15

x= 13

7 0
2 years ago
Read 2 more answers
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