SOLUTION: f(x) = (-100e^-0.25x) - 50x (b) Determine the location of all critical points and determine their nature for the function

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Question 1193035: f(x) = (-100e^-0.25x) - 50x
(b) Determine the location of all critical points and determine their nature for the function
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
graph it.
graph%28300%2C300%2C-10%2C5%2C-500%2C10%2C%28-100e%5E%28-0.25x%29-50x%29%29
f'(x)=0.25*e^(-0.25x)-50
set equal to 0.
50=25e^(-0.25x)
2=e^(-0.25x)
ln 2=-0.25x
0.693=-0.25x
x=-2.77
f(x)=-61.37
second derivative is -6.25e^(-0.25x)
where x=-2.77 the second derivative is negative. This is a maximum.