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Bond [772]
3 years ago
11

Need help and explain please!!

Mathematics
1 answer:
lukranit [14]3 years ago
3 0

Answer:

x=-4\text{ and } x=3

Step-by-step explanation:

We are given the second derivative:

g''(x)=(x-3)^2(x+4)(x-6)

And we want to find its inflection points.

To do so, we will first determine possible inflection points. These occur whenever g''(x) = 0 or is undefined.

Next, we will test values for the intervals. Inflection points occur if and only if the sign changes before and after the point.

So first, finding the zeros, we see that:

0=(x-3)^2(x+4)(x-6)\Rightarrow x=-4, 3, 6

So, we can draw the following number-line:

<----(-4)--------------(3)----(6)---->

Now, we will test values for the intervals x < -4, -4 < x < 3, 3 < x < 6, and x > 6.

Testing for x < -4, we can use -5. So:

g^\prime^\prime(-5)=(-5-3)^2(-5+4)(-5-6)=704>0

Since we acquired a positive result, g(x) is concave up for x < -4.

For -4 < x < 3, we can use 0. So:

g^\prime^\prime(0)=(0-3)^2(0+4)(0-6)=-216

Since we acquired a negative result, g(x) is concave down for -4 < x < 3.

And since the sign changed before and after the possible inflection point at x = -4, x = -4 is indeed an inflection point.

For 3 < x < 6, we can use 4. So:

g^\prime^\prime(4)=(4-3)^2(4+4)(4-6)=-16

Since we acquired a negative result, g(x) is concave down for 3 < x < 6.

Since the sign didn't change before and after the possible inflection point at x = 3 (it stayed negative both times), x = -3 is not a inflection point.

And finally, for x > 6, we can use 7. So:

g^\prime^\prime(7)=(7-3)^2(7+4)(7-6)=176>0

So, g(x) is concave up for x > 6.

And since we changed signs before and after the inflection point at x = 6, x = 6 is indeed an inflection point.

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Virty [35]

Answer:

0 ≤ x < 1.12 and 34.18 < x ≤ 39.87

Step-by-step explanation:

Let

x ----> is the number of tires produced, in thousands

C(x) --->  the production cost, in thousands of dollars

we have

C(x)=-0.34x^{2} +12x+62

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The graph in the attached figure

we know that

Looking at the graph

For the interval [0,1.12) -----> 0\leq x

The value of C(x) ----> C(x) < 75

That means ----> The production cost is under $75,000

For the interval (34.18,39.87] -----> 34.18 < x\leq 39.87

The value of C(x) ----> C(x) < 75

That means ----> The production cost is under $75,000

Remember that the variable x (number of tires) cannot be a negative number

therefore

If the company wants to keep its production costs under $75,000 a reasonable domain for the constraint x is

0 ≤ x < 1.12 and 34.18 < x ≤ 39.87

7 0
3 years ago
Question 21 is probably the hardest question on this homework
Snezhnost [94]
-15+5x= 20

5x= 35
x= 7

20= -15+5x

35= 5x

7 = x
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3 years ago
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Help me please,Thanks
ehidna [41]
The answer is 1/16 i think. Hope this helps! :)
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3 years ago
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Carl and rita at breakfast at the local diner. Their bill came to $11.48. They gave their waitress a tip that wad 25% of the bil
WINSTONCH [101]

Answer:

(11.48*25%)+11.48


Step-by-step explanation:


4 0
3 years ago
The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by hal
Leto [7]

Since the length of this rectangle is twice its breadth, the length is equal to 40 cm.

<h3>How to calculate the area of a rectangle?</h3>

Mathematically, the area of a rectangle can be calculated by using this formula:

Area = Length × Width

Based on the information provided, we have:

  • Its length is decreased half of the 10 cm ⇒ (length - 5)
  • Its breadth is increased by half of the 10 cm ⇒ (breadth + 5)
  • Its area is increased by 75 cm ⇒ (area + 5)

Substituting the parameters into the formula, we have:

LB + 75 = (L - 5)(B + 5)

2B² + 75 = (2B - 5)(2B + 5)

2B² + 75 = 2B(B + 5) - 5(B + 5)

2B² + 75 = 2B² + 10B - 5B - 25

5B = 75 + 25

5B = 100

B = 100/20

B = 20 cm.

For the length, we have:

L = 2B

L = 2 × 20

L = 40 cm.

Read more on rectangle here: brainly.com/question/25292087

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