math question - another one.

[Scrapster]

Here's my function:

y=(-3+sqroot(-4e^x+8x+13))/2

Question: Determine where the solution attains its maximum value.

I'm not sure how I should start figuring it out. Should I just start pluging in numbers or should I start somewhere specific?

Any ideas? (graphing tips, hints, cheats, etc..)

Scrapster

 

[madmacks]

take the derivative and see how it works when it approaches zero... something like that, i forgot. too long ago...

 

[Scrapster]

Someone else mentioned that if I take the derivative and solve for zero I will get the maximum. This solution may be right, but then I wonder about how you find the minimum value?
Anyways, can anyone confirm this is the correct method for finding the maximum value of a function?

Scrapster

 

[madmacks]

theres a bunch of conditions <1,>1,0, infinity leading to different results... it should be all in your book. if you dont have one the that sucks.

 

[Viper GTS]

Take the derivative, &amp; solve that equation for all the y-intercepts. These will be the maximum &amp; minimum values of the equation. Substitute the respective x-values &amp; get the corresponding y-values. Then just pick the largest y-value &amp; you've got your coordinates.

Viper GTS

 

[Mday]

when the first derivative is 0, the function achives what is called a critical point. this is where the tangent to the curve of the function is the horizontal line.

it can be either a min or a max (relative or absolute), and you should verify the min and max with the second derivative which tells you the concavity or test points between those values of X for which the first derivative is zero.

when it is an absolute MAX, it is the max value that function can attain. when it is a relative max, it means there can be other values for which the function is greater, but that relative max is greater than the values around it.

also, it can be that the function's maximum value is infinite. as in f(x) = x^2 which only has ONE critical point for when the f' = 0, which is x=0, which is an absolute min.