anonymous
  • anonymous
determine if f has a maximum value or a minimum value; b. the value of x at which the maximum or minimum occurs; c. the maximum or minimum value of f for f(x)=-x^2-x-4
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
In case of second degree polynomial, like the one we have, f has a maximum value if the coefficient of x^2 is negative. So f has a maximum value, and does not have a minimum.
anonymous
  • anonymous
Okay
anonymous
  • anonymous
To determine at which value of x the maximum value occurs, you need to find the derivative and solve for it when it's equal to zero: \[f'(x)=-2x-1=0\] solve this last equation for x, that will be the the value of x at which the maximum occurs.

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anonymous
  • anonymous
I'm lost, i'm sorry
anonymous
  • anonymous
Ok. \[-2x-1=0 \implies 2x=-1 \implies x=-1/2\] at x=-1/2 f has its maximum value. (that's the answer of part b).
anonymous
  • anonymous
part c. the maximum value of occurs at x=-1/2. So, f(-1/2) is the maximum value. That's: \[f(-1/2)=-(-1/2)^2-(-1/2)-4=-1/4+1/2-4=-15/4\]
anonymous
  • anonymous
Wow..Okay
anonymous
  • anonymous
You're welcome :P I hope that makes sense to you.
anonymous
  • anonymous
So, a would be maximum considering b and c are both maximun..is that right
anonymous
  • anonymous
I do appreciate your help and thank you so very much.
anonymous
  • anonymous
Yeah!

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