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3 years ago

How does g(x) 2 change over the interval from x = 0 to x = 2?

Mathematics

1 answer:

kobusy [5.1K]3 years ago

5 0

Answer:

Step-by-step explanation:

This means that the average of all the slopes of lines tangent to the graph of g(x) between (4 ,15) and (6 ,33) is 9.

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3 years ago

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4 years ago

Need help and explain please!!

lukranit [14]

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.

3 0

3 years ago

There are two aircraft carriers, A and B, and the carrier A is longer in length the carrier B. The total length of these two car

Svetradugi [14.3K]

Answer:

<h3>Length of carrier A = 2096 feet</h3><h3> Length of carrier B=2082 feet.</h3>

Step-by-step explanation:

Given , two air craft carriers are A and B . The carrier A is longer than the carrier B in length.

Total length of two carriers =4178 feet

Difference of two carriers = 14 feet

Let

Length of carrier A =x feet

And

Legth of carrier B =y feet

According to question

The I equation is

x+y=4178

The II equation is

x-y= 14

Substitution method: In this method step I : we find value of x or y from the equation I

Step II: put the value of x or y in II equation then we get the value of another varaiable x or y

Step : Again put the obatined value of variable x or y from step II in equation I then we get value of other variable x or y .

By using substitution method ,

we find value of x from equation I

x= 4178-y

Now, put the value of x in equation II then we get

4178-y-y=14

4178-2y=14

4178-14=2y

4164=2y

$y=\frac{4164}{2}$

y= 2082

Again , put the value of y in equation I

2082 +x=4178

x= 4178-2082

x=2096

Hence, the length of carrier A = 2096 feet

The length of carrier B= 2082 feet

4 0

3 years ago