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sattari [20]
2 years ago
14

(a)Use differentiation to find the minimum value of f(x)= 3x^2 - 5x + 10 and the value(s) of x for which this minimum occurs.

Mathematics
1 answer:
elena-14-01-66 [18.8K]2 years ago
3 0

Hi there!

Begin by differentiating f(x) using the power rule:

dy/dx = nxⁿ⁻¹

Therefore:

f(x) = 3x² - 5x + 10

f'(x) = 6x - 5

Set this equation equal to 0 to find the x-intercept:

0 = 6x - 5

5 = 6x

x = 5/6, which is where the graph goes from NEGATIVE to POSITIVE, so there is a MINIMUM at this value.

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Express this to single logarithm
zzz [600]

Answer:  \log_{2}\left(\frac{q^2\sqrt{m}}{n^3}\right)

We have something in the form log(x/y) where x = q^2*sqrt(m) and y = n^3. The log is base 2.

===========================================================

Explanation:

It seems strange how the first two logs you wrote are base 2, but the third one is not. I'll assume that you meant to say it's also base 2. Because base 2 is fundamental to computing, logs of this nature are often referred to as binary logarithms.

I'm going to use these three log rules, which apply to any base.

  1. log(A) + log(B) = log(A*B)
  2. log(A) - log(B) = log(A/B)
  3. B*log(A) = log(A^B)

From there, we can then say the following:

\frac{1}{2}\log_{2}\left(m\right)-3\log_{2}\left(n\right)+2\log_{2}\left(q\right)\\\\\log_{2}\left(m^{1/2}\right)-\log_{2}\left(n^3\right)+\log_{2}\left(q^2\right) \ \text{ .... use log rule 3}\\\\\log_{2}\left(\sqrt{m}\right)+\log_{2}\left(q^2\right)-\log_{2}\left(n^3\right)\\\\\log_{2}\left(\sqrt{m}*q^2\right)-\log_{2}\left(n^3\right) \ \text{ .... use log rule 1}\\\\\log_{2}\left(\frac{q^2\sqrt{m}}{n^3}\right) \ \text{ .... use log rule 2}

8 0
2 years ago
Solve for x.<br> 6 - 4x = -22
Kitty [74]

Answer:

x = 7

Step-by-step explanation:

6 - 4x = -22

-6          - 6

-4x = -28

x = -28/-4

x = 7

8 0
3 years ago
Four more than twice a number<br><br>a.2x+4<br><br><br>b.4x+2<br><br>c.6x<br><br>d.2x &gt; 4​
makkiz [27]

Answer:

a. 2x + 4

Step-by-step explanation:

Four more than twice a number

Let x = unknown number

Four more than twice of x

Twice of x can be written as 2x

Four more than 2x

Four more can be written as + 4

We get 2x + 4

6 0
2 years ago
A stadium holds 50,000 people.The stadium is divided into 250 different seating sections.How many seats are in each section?
worty [1.4K]
50,000 ÷ 250 = 200

This means that there are 200 seats in each section.
8 0
2 years ago
Read 2 more answers
Which equation has the same solution as 2x^2+16x-10=0
dmitriy555 [2]
D
Divide the whole thing by 2
2(X^2+8x-5)
X^2+8x. =5
Half of 8 is 4 sq it so you add 16
X^2+8x+16= 5+16
(X+4)^2=21
8 0
2 years ago
Read 2 more answers
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