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anonymous
 5 years ago
Consider the function f(x) = 8 √{ x} + 9 on the interval [ 2 , 8 ]
(A) Find the average or mean slope of the function on this interval
(B) By the Mean Value Theorem, we know there exists at least one c in the open interval ( 2 , 8 ) such that f′( c) is equal to this mean slope. Find all values of c that work and list them (separated by commas) in the box below.
anonymous
 5 years ago
Consider the function f(x) = 8 √{ x} + 9 on the interval [ 2 , 8 ] (A) Find the average or mean slope of the function on this interval (B) By the Mean Value Theorem, we know there exists at least one c in the open interval ( 2 , 8 ) such that f′( c) is equal to this mean slope. Find all values of c that work and list them (separated by commas) in the box below.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea this is one of the ones i am having trouble on...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0mean slope means what? the slope of the line from end point to end point?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i don't know i check all my notes and no where do i see mean slope so i don't know why the teacher assigned this problem

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I believe that it means the average slope between the intervals and is found by taking the slope of the line between the end points.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then you find a point in the interval that touches the graph at one point with that slope

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so what would be the equation to find the slope between the intervals

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(8)  f(2) change in y  over 82 change in x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0this is how you find any slope of a line :) the change in y over the change in x

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0whats our mean slope? I get: 4sqrt(2)  3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when f'(c) = 4sqrt(2)/3 then we have found the values for "x" that satisfy the problem

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats what i got...it was correct

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(x) = 8x^(1/2) + 9 whats our derivative?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yay!!... 4sqrt(x) 4sqrt(2)  =  we need to solve this then x 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.012 sqrt(x) = 4x sqrt(2) ; divide both sides by 4 3 sqrt(x) = x sqrt(2)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the answer is 4.5....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0did you solve it, or is that what we are going for?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i solved it...well after you help of course...i started to see the problem working out...i got another...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I was gonna square both sides and do some magic :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=(x3)(x7)^3+8\] we are looking for absolute max and min for intervals at [1,4] and [1,8] and [4,9]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0.... i got 9/2...... so nyahh!!

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0.......ok, i can read..... sometimes :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0its a quartic equation which will resemble a "W" perhaps

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0just expand it and make it easier for ya...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok..lol... i got \[f'(x)=(x7)^3+(x3)(3)(x7)^2\]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(x) = x^4 24x^3 +210x^2 784x +1037 f'(x) = 4x^3 72x^2 +420x 784 :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0your way might be easier to read :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so i would make the equation equal to zero right???

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0x = 7 is a zero, thats easy to see

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and would 3 be a zero

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03 would be a zero + (7)^3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0take the second derivative to see how the graph is behaving

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f''(x) = 12x^2 144x +420

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0factor out a 12.. 12(x^2  12x + 35)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.012(x7)(x5) is the factored form

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok and how would i use that to find the max and min between all three intervals

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0draw a number line straight across the paper......

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0<..................5......................7....................>

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0at 5 and 7 we have inflection points...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok but our first interval were looking at is [1,4]

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0<..................5......................7....................>  +++ +++   +++  +  + when we multiply these "zones" together, we get these results

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0do you undertand this diagram?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea...how do we apply the intervals to this...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0[1,4] is in an area that is concave up, so if anything it would have a MIN in it someplace

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Now, are we looking for the "highest and or lowest point in the intervals?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am going to break up the question like it is.... f(x)=(x−3)(x−7)^3+8 a. interval [1,4] absolute max: absolute min: this is how all of the other ones are

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0our graph is acting like this:

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0solve for f(1) and f(4) to see what our values are.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0f(1) = 440 if I did it right

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the max is at (1,440)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0here a thought, plug in 4 into the derivative and see if we get a zero :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, 4 is a zero for f'(x)...im a genuis :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0[1,4] (1 ,440) = max and (4,19) = min you agree?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0and the graph doesnt have an more "bumps in it, just some transitional bends.....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea the next interval is the same and the last one the max is (9,56) and min is (4,19)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=(3+9\ln (x))/x\] i need to find the x coordinate of the absolute max...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0start a new question, I think this ones lagging alot becasue of all the "replies" its trying to keep track of :)
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