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anonymous
 5 years ago
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^2x4
anonymous
 5 years ago
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^2x4

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In 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
 5 years ago
Best ResponseYou've already chosen the best response.0To 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: \[f'(x)=2x1=0\] solve this last equation for x, that will be the the value of x at which the maximum occurs.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok. \[2x1=0 \implies 2x=1 \implies x=1/2\] at x=1/2 f has its maximum value. (that's the answer of part b).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0part c. the maximum value of occurs at x=1/2. So, f(1/2) is the maximum value. That's: \[f(1/2)=(1/2)^2(1/2)4=1/4+1/24=15/4\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You're welcome :P I hope that makes sense to you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, a would be maximum considering b and c are both maximun..is that right

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I do appreciate your help and thank you so very much.
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