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marshall1432

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f(x)=-x^2+10x-3

I need to find the maximum or minimum value.

Isn't this one a minimum value because it begins with a negative? Is the value -1?

Also,

The sum of the length l and the width w of a rectangular area is 240 meters.

a. Write w as a function of l
b. Write the area A as a function of l.
c. Find the dimensions that produce the greatest area.


a. w(l)= l x w=240m
b. l(240)=l x w
c. 40 x 6

HELP! Thanks
 
marshall1432 said:
f(x)=-x^2+10x-3

I need to find the maximum or minimum value.

Isn't this one a minimum value because it begins with a negative? Is the value -1?
No....the negative coefficient of x^2 tells us that the parabola opens DOWNWARD, so it looks kind of like an upside-down U. Thus, it has a maximum value, and that occurs at the vertex of the parabola. You can find the x-coordinate of the vertex, which is x = -b/2a. Then substitute that value for x in the function, and you will get the maximum value of the function. And no, it is NOT -1.

Also,

The sum of the length l and the width w of a rectangular area is 240 meters.

a. Write w as a function of l
b. Write the area A as a function of l.
c. Find the dimensions that produce the greatest area.


a. w(l)= l x w=240m No. The problem states that the SUM of l and w is 240. So, l + w = 240, and w = 240 - l
b. l(240)=l x w Area = l*w Substitute (240 - l) for w, and you get
Area = (240 - w)*w, or
Area = -w^2 + 240w
c. 40 x 6

You will need to find the maximum value of the function A = -w^2 + 240w
It's a parabola which opens downward; find the w-value at the vertex, and then use that to find the length.

HELP! Thanks
Click to expand...
 
Mrspi said:
marshall1432 said:
f(x)=-x^2+10x-3

I need to find the maximum or minimum value.

Isn't this one a minimum value because it begins with a negative? Is the value -1?
No....the negative coefficient of x^2 tells us that the parabola opens DOWNWARD, so it looks kind of like an upside-down U. Thus, it has a maximum value, and that occurs at the vertex of the parabola. You can find the x-coordinate of the vertex, which is x = -b/2a. Then substitute that value for x in the function, and you will get the maximum value of the function. And no, it is NOT -1.

Also,

The sum of the length l and the width w of a rectangular area is 240 meters.

a. Write w as a function of l
b. Write the area A as a function of l.
c. Find the dimensions that produce the greatest area.


a. w(l)= l x w=240m No. The problem states that the SUM of l and w is 240. So, l + w = 240, and w = 240 - l
b. l(240)=l x w Area = l*w Substitute (240 - l) for w, and you get
Area = (240 - w)*w, or
Area = -w^2 + 240w
c. 40 x 6

You will need to find the maximum value of the function A = -w^2 + 240w
It's a parabola which opens downward; find the w-value at the vertex, and then use that to find the length.

HELP! Thanks
Click to expand...
Click to expand...

SO THEN IT HAS A MAXIMUM VALUE OF 5.....BECAUSE -B/2A EQUALS -10/2(-1)=5

WHAT ABOUT A B AND C. WHAT ARE YOU SAYING ON THOSE?
 
The x-coordinate of the vertex is 5. BUT....you apparently didn't read the rest of the response, where I said "Then substitute that value for x in the function, and you will find the maximum value of the function."

f(x) = -x^2 + 10x - 3
f(5) = - 5^2 + 10(5) - 3
f(5) = -25 + 50 - 3
f(5) = 22

And I apologize for an error I made in parts b and c.....I gave the area as a function of w, not L.

A = L*w
w = 240 - L
A = L(240 - L)
A = -L^2 - 240L
We now have the area as a function of the length L.

This is a parabola opening down. Find the L coordinate of the vertex, which is at L = -b/2a.

This is the value of L, the length, that gives a maximum area. You also need the width; that can be obtained from the fact that w = 240 - L
 
marshall1432 said:
forget it...that didnt answer any of the questions iasked.
Click to expand...
Actually, your questions were answered, and quite completely. Granted, you were not provided with the fully-worked solution to copy down, at least not for all three parts. But you shouldn't need that.

If you are so lost and/or behind that you cannot understand the replies you were given, then I'm afraid you need much more help than we can provide. Please consider hiring a tutor. By working face to face a few hours a week (daily would be best), you may be able to get caught up inside a month.

Good luck! :D

Eliz.
 
um...did you forget that:

-5^2 is not 25 but -25 because a negative times a negative is a positive...???
 
marshall1432 said:
um...did you forget that: -5^2 is not 25 but -25 because a negative times a negative is a positive...???
Click to expand...
Um... What does this have to do with anything...?

Please clarify. Thank you! :D

Eliz.
 
yeah, it wouldnt make sense to you because you were not helping me with the problem...go back up and look at the first problem i asked f(5)=22 and then it will make sense bc that is the wrong answer!
 
marshall1432 said:
yeah, it wouldnt make sense to you because you were not helping me with the problem...go back up and look at the first problem i asked f(5)=22 and then it will make sense bc that is the wrong answer!
Click to expand...

Please tell us what the correct answer is.
 
Subhotosh Khan said:
marshall1432 said:
yeah, it wouldnt make sense to you because you were not helping me with the problem...go back up and look at the first problem i asked f(5)=22 and then it will make sense bc that is the wrong answer!
Click to expand...

Please tell us what the correct answer is.
Click to expand...

f(5)=-5^2+10(5)-3
f(5)=25+50-3
f(5)=75-3
f(5)=72
 
marshall1432 said:
um...did you forget that:

-5^2 is not 25 but -25 because a negative times a negative is a positive...???
Click to expand...

negative times a negative is a positive - only comes in (related to your problem) if you are doing

(-5)^2 = (-5) * (-5) = 25

But if you have

-(5)^2 = -(5*5) = -25

Then you do not have "negative times negative" situation.


Which case are referring to?!
 
Subhotosh Khan said:
marshall1432 said:
um...did you forget that:

-5^2 is not 25 but -25 because a negative times a negative is a positive...???
Click to expand...

negative times a negative is a positive - only comes in (related to your problem) if you are doing

(-5)^2 = (-5) * (-5) = 25

But if you have

-(5)^2 = -(5*5) = -25

Then you do not have "negative times negative" situation.


Which case are referring to?!
Click to expand...

the problem is
f(x)=-x^2+10x-3

idk which one is it you think?
 
marshall1432 said:
Subhotosh Khan said:
marshall1432 said:
yeah, it wouldnt make sense to you because you were not helping me with the problem...go back up and look at the first problem i asked f(5)=22 and then it will make sense bc that is the wrong answer!
Click to expand...

Please tell us what the correct answer is.
Click to expand...

f(5)=(-5)^2+10(5)-3
f(5)=25+50-3 <--- only if the parentheses above are present
f(5)=75-3
f(5)=72

Review carefully "order of operations".
Click to expand...
 
the problem is
f(x)=-x^2+10x-3

This is equivalent to:

f(x) = (-1) * x^2 + 10*x - 3


The coefficient of x^2 term is (-1)

Now think again

idk which one is it you think?[/quote]
 
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