Question

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

Answer 1

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.

Answer 2

Okay

Answer 3

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.

Answer 4

I'm lost, i'm sorry

Answer 5

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).

Answer 6

part c.
the maximum value of occurs at x=-1/2. So, f(-1/2) is the maximum value. That's:
\[f(-1/2)=-(-1/2)^2-(-1/2)-4=-1/4+1/2-4=-15/4\]

Answer 7

Wow..Okay

Answer 8

You're welcome :P I hope that makes sense to you.

Answer 9

So, a would be maximum considering b and c are both maximun..is that right

Answer 10

I do appreciate your help and thank you so very much.

Answer 11

Yeah!