Question

f(x)=-x^2-x-4

Determine
a. if f has a maximum value or a minimum
b. the value of x at which the max or min occurs
c. the max or min value of f

Answer 1

just graph it

Answer 2

the parabola is oven downward so we have an upside down U
that means we have a max

Answer 3

open*

Answer 4

a. maximum
b. x = -1/2
c. -9/2

Answer 5

A) derive, set equal to zero. There will be two. Test both critical points. If it goes from positive to negative, it's a max. If it's opposite, it's a min. If there is no change, which there won't be in this instance, it tells you nothing.
B) the values you tested in a.
C) plug the values in from b and solve for y.

Answer 6

f(x)=-(x^2+x)-4=-(x^2+x+(1/2)^2)-4+(1/2)^2
=-(x+1/2)^2-4+1/4=(x+1/2)^2-15/4
so the vertex=(-1/2,-15/4)

Answer 7

Correction, theres one critical point.