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erica [24]
3 years ago
9

Find the local maximum and two local minima of the graph of the following function.

Mathematics
1 answer:
Archy [21]3 years ago
5 0

Answer:

max is (3, 1) and min are (2, 0) and (4, 0)

Step-by-step explanation:

Since there is no bounds on this (not a closed interval), the only max and min we can find are local.  The max and min points exist where the first derivative of the function is equal to 0.  That means that we have to find the first derivative.  That is:

y'=4x^3-36x^2+104x-96

If you factor this higher-degree polynomial (I used the Rational Root Theorem and then synthetic division), you find that the zeros of the derivative exist at the x values of

2, 3, 4

Therefore, f(2), f(3), and f(4) will either be max values or min values.

f(2) = 0 so the point is (2, 0)

f(3) = 1 so the point is (3, 1)

f(4) = 0 so the point is (4, 0)

As you can see, the max point is (3, 1)

the min points are (2, 0) and (4, 0)

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Compare the fraction 3/5 to 1/2 and then compare 2/6 to 1/2. Use symbols in your answer
worty [1.4K]
Hello there!

"Compare the fraction 3/5 to 1/2 and then compare 2/6 to 1/2. Use symbols in your answer"


To make this easier, we will make it so that both fractions in each pair has like bases.

To make 3/5 and 1/2 have a like base, we must make the denominators 10. To do this, we will do the following:

(3*2)/(5*2) = 6/10

(1*5)/(2*5) = 5/10

Now we can easily compare and not worry about the denominator

So, let's just look at the numerators. 

Which is greater, 5 or 6? We know 6 is greater, so:

6/10 > 5/10

That means:

3/5 > 1/2

Now, we must do the same for 2/6 and 1/2

We will make them both 6. So, we can leave 2/6 alone

2/6

(1*3)/(2*3) = 3/6

Now we have 2/6 and 3/6

Which is greater, 3 or 2. The answer to that is 2. So:

3/6 > 2/6

This means that 1/2 > 2/6


Our answers are:

1. 3/6 > 2/6

2. 1/2 > 2/6


I hope I was able to help you!

~ Fire




7 0
3 years ago
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