SOLUTION: Let f (x) = x^2 − 5/x Find all extreme values (if any) of f on the interval [1, 5). Determine at which numbers in the interval these values occur. Enter DNE in any unused

Algebra ->  Equations -> SOLUTION: Let f (x) = x^2 − 5/x Find all extreme values (if any) of f on the interval [1, 5). Determine at which numbers in the interval these values occur. Enter DNE in any unused      Log On


   

Question 996108: Let f (x) = x^2 − 5/x
Find all extreme values (if any) of f on the interval [1, 5). Determine at which numbers in the interval these values occur. Enter DNE in any unused answer blanks.
The maximum value f attains on the interval [1, 5) occurs at x = ?
The maximum value is ?
The minimum value f attains on the interval [1, 5) occurs at x = ? The minimum value is ?
Please show how you solved
Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm going to assume the equation is f%28x%29+=+x%5E2+-+5%2Fx+


f(x) = x^2 - 5/x
f(x) = x^2 - 5x^(-1)
f ' (x) = 2x^(2-1) - (-1)*5x^(-1-1) ... apply derivative
f ' (x) = 2x + 5x^(-2)
f ' (x) = 2x + 5/(x^2)
0 = 2x + 5/(x^2) ... plug in f ' (x) = 0 and solve for x
0 = 2x*(x^2/x^2) + 5/(x^2)
0 = (2x^3)/(x^2) + 5/(x^2)
0 = (2x^3+5)/(x^2)
(2x^3+5)/(x^2) = 0
2x^3+5 = 0
2x^3 = -5
x^3 = -5/2
x = root%283%2C-5%2F2%29
x = -1.35720880829746 ... this is approximate


The problem asks to "Find all extreme values (if any) of f on the interval [1, 5)" but the critical value x = -1.35720880829746 is NOT in that interval at all. So there are NO extreme values in that interval.