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anonymous
 one year ago
The figure below shows the graph of f ′, the derivative of the function f, on the closed interval from x = −2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4.
Find the xvalue where f attains its absolute maximum value on the closed interval from x = −2 to x = 6. Justify your answer
anonymous
 one year ago
The figure below shows the graph of f ′, the derivative of the function f, on the closed interval from x = −2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4. Find the xvalue where f attains its absolute maximum value on the closed interval from x = −2 to x = 6. Justify your answer

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1439314511563:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439314520378:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2what do you know about the relationship between first derivative and relative min/max ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wherever the first derivative = zero their is likely a max min , where the first derivative is negative and then positive the function is concave down and the inverse of that to indicate concave up

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0umm thats pretty much it, am i missing something

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2that looks good, look at the given graph of first derivative notice that the first derivative stays negative in the interval [2, 5], this means the function is "decreasing" in this interval, yes ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2we cannot have any max/min in the interval (2, 5) since the function is continuously decreasing

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2what about the point (5, 0) does that mean the function has a min or max at x=5 ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2good, since the first derivative is going form "negative" to "positive", the function will have a local minimum at x=5

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2that essentially means, we do not have any local maximums in the interval (2, 6)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2so the absolute maximum must occur at the boundary points

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well it just kept increasing after x = 4 so i figured it would be the highest , but i guess x=2 could be just as high because we don't know what happened before x = 2 right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Notice that the first derivative is "negative" in the interval (2, 5) that means the actual function is "decreasing" in the interval (2, 5)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay i see so your suggesting that because it decreased for such a long interval and then increased for such a short interval the maximum would be ant x = 2 is that what your saying?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Kindof! but thats not it, at this point, i do believe the function attains its maximum at x = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay well why do you suggest its x = 2?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1439315773571:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2which area do you think is more black or red ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2That means the actual function did not recover the fall yet

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2so x=2 is indeed the absolute maximum

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay that makes sense

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2If you're good with definite integrals, notice below : \[f(6)f(2) = \int\limits_{2}^6f'(x)\,dx \lt 0\] that implies \(f(6)\lt f(2)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay thanks for the help!
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