SOLUTION: Determine the location and value of the absolute extreme values of f on the given interval, if they exist. f(x) =4sqrt(x) −8x^2/x on [1,10]

Algebra ->  Test -> SOLUTION: Determine the location and value of the absolute extreme values of f on the given interval, if they exist. f(x) =4sqrt(x) −8x^2/x on [1,10]      Log On


   

Question 1158623: Determine the location and value of the absolute extreme values of f on the given interval, if they exist.
f(x) =4sqrt(x) −8x^2/x
on [1,10]
Answer by KMST(5396) About Me  (Show Source):
You can put this solution on YOUR website!
The function f(x)=4sqrt(x)−8x^2/x is not a very interesting one, and may not the the function intended.
I suspect the function intended could have been f(x)=(4sqrt(x)-8x^2)/x , which means f%28x%29%22=%22%284sqrt%28x%29-8x%5E2%29%2Fx , also not an interesting function.
The domain of f(x)=(4sqrt(x)-8x^2)/x is x%3E0 , which can be expressed as %22%280%2C%22infinity%22%29%22 .
The graph of f%28x%29%22=%22%7D%7D%7B%7B%7B%284sqrt%28x%29-8x%5E2%29%2Fx%22=%224%2Fsqrt%28x%29-8x is graph%28300%2C200%2C-2%2C13%2C-90%2C10%2C%284sqrt%28x%29-8x%5E2%29%2Fx%29
The derivative is negative throughout the domain of the function, meaning that the function decreases continuously.
Its absolute extremes in the interval [1, 10] are
f%281%29%22=%22%284sqrt%281%29-8%2A1%5E2%29%2F1%22=%22%284%2A1-8%29%2F1%22=%22%284-8%29%2F1%22=%22%28-4%29%2F1=highlight%28-4%29 , a maximum, and
f%2810%29%22=%22%284sqrt%2810%29-8%2A10%5E2%29%2F10%22=%22%284sqrt%2810%29-8%2A100%29%2F10, a minimum, with a rounded value of highlight%28-67.35%29

The domain of f(x)=4sqrt(x)−8x^2/x is %22%280%2C%22infinity%22%29%22 .
That function is f%28x%29=4sqrt%28x%29-8x%5E2%2Fx%22=%22system%284sqrt%28x%29-8x%2Cx%3E0%29
Its graph is graph%28300%2C200%2C-2%2C13%2C-90%2C10%2C4sqrt%28x%29-8x%29
The derivative is negative throughout the domain of the function, meaning that the function decreases continuously.
Its absolute extremes in the interval [1, 10] are
f%281%29=4sqrt%281%29-8%2A1=4%2A1-8=4-8=highlight%28-4%29 , a maximum, and
f%2810%29=4sqrt%2810%29-8%2A10=highlight%284sqrt%2810%29-8%29, a minimum, with a rounded value of highlight%28-78.735%29