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pishuonlain [190]
2 years ago
12

PLEASE HELP?

Mathematics
1 answer:
const2013 [10]2 years ago
6 0

Answer:

When we have a function g(x)

We will have a maximum at x when:

g'(x) = 0

g''(x) < 0.

Now we start with:

g(x) = 3*x^4 - 8*x^3

The first derivation is:

g'(x) = 4*3*x^3 - 3*8*x^2

g'(x) = 12*x^3 - 24*x^2

We can rewrite this as:

g'(x) = x^2*(12*x - 24)

Now we want to solve:

g'(x) = 0 =  x^2*(12*x - 24)

We have one trivial solution, that is when x = 0.

The other solution will be when the term inside of the parentheses is equal to zero.

Then we need to solve:

12*x - 24 = 0

12*x = 24

x = 24/12 = 2

Then g'(x) is equal to zero for x = 0, and x = 2.

Notice that both of these points are included in the interval [ -2,2 ]

Now we need to look at the second derivative of g(x):

g''(x) = 3*12*x^2 - 2*24*x

g''(x) = 36*x^2 - 48*x

Ok, now we need to evaluate this in the two roots we found before:

if x = 0:

g''(0) = 36*0^2 - 48*0 = 0

g''(0) = 0

Then we do not have a maximum at x = 0, this is a point of inflection.

if x = 2:

g''(2) = 36*(2^2) - 48*2 = 48

then:

g''(2) > 0

This is an absolute minimum.

Now let's look only at the interval [ -2,2 ]

We know that:

g''(0) =  0

g''(2) > 0

Then at some point, we should have g''(x) < 0 in our interval.

We need to find the first point such that happens, so let's try with the lower limit of the interval but with the first derivation, if g'(x) < 0, this means that the function is decreasing from that point on, then that point will be a maximum in our interval.

x = -2

g'(-2) = (-2)^2*(12*-2 - 24) = -192

And if we look at the function:

g'(x) = x^2*(12*x - 24)

We can easily see that it is negative unitl x = 0, and then it keeps being negative until x = 2.

So in the interval  [ -2,2 ], the function g'(x) is always negative or zero, this means that in the interval  [ -2,2 ], the function g(x) is always decreasing or constant.

Then the absolute maximum of g(x) in the interval  [ -2,2 ]  will be  x = -2

this means that:

g(-2) ≥ g(x) for all x ∈  [ -2,2 ]

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steposvetlana [31]

Answer:

36 ÷ a

55 - b

18 + c

49 x d

e ÷ 62

Step-by-step explanation:

7 0
2 years ago
Express as -80/112 as a rational: numerator = -5​
Anastasy [175]

Answer:

-80\112 = -5\7

we divided both numbers by 16

8 0
3 years ago
Sally buys a handbag. there was a discount of 30%. if sally paid, $17.50, what was the original price?
andrew11 [14]
The original price was $25. 

First, convert the 30% to a real mathematical number. For percents, this is always done by dividing the 30% by 100%, or 30% / 100% = 0.300.

Second, find out what 30% of $25 is. This is the amount of the sale discount. This is always found by mulitplying 0.300 by the item's cost $25, like this:

0.300 x $25 = $ 7.50.

So for this sale, you'll save $ 7.50 on this item.

This means, the cost of the item to you is

<span>$25 - $ 7.50 = $17.50.</span>
6 0
3 years ago
FIND M∠R (GIVING BRAINLIEST, 25 PTS)
riadik2000 [5.3K]

Answer:

<h2>76</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • triangles
  • equation
  • PEMDAS
<h3>given:</h3>
  • M\angle T=2x+2
  • M\angle R=3x+1
<h3>tips and formulas:</h3>
  • this is an isosceles triangle since two sides are equal therefore \angle T=\angle S
  • a triangle contains 180°
<h3>let's solve:</h3>

according to the question

2x+2+2x+2+3x+1=180

solve:

  1. collect like terms:7x+5=180
  2. substract 5 from both sides:=>7x+5-5=180-5=>7x=175
  3. divide both sides by 7: =>7x/7=175/7
  • x=25

given:

M∠R=3x+1

substitute the value of x

3×25+1

75+1

76

7 0
2 years ago
Read 2 more answers
3. Find the least common denominator for the group of denominators using the method of prime numbers. 45, 75, 63​
Sloan [31]

We have to find LCM

3 | 45,75,63

3 | 15,25,21

5 | 5,25,7

5 | 1,5,7

7 | 1,1,7

LCM=3×3×5×5×7=1575

8 0
2 years ago
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