Calculus
posted by Anonymous
Find the open intervals on which f(x) = 6x^2 + 96x + 7 is increasing or decreasing.
a. increasing on (inf, 16); decreasing on (16, inf).
b. increasing on (inf, 14); decreasing on (14, inf).
c. increasing on (inf, 84); decreasing on (84, inf).
d. increasing on (inf, 56); decreasing on (56, inf).
e. increasing on (inf, 8); decreasing on (8, inf).
I think the answer is e, but the answer is still greater than 0 when x = 10 is used?

Damon
this is a parabola
since we have a negative coef of x^2
it opens down (sheds water)
the real question is, where is the vertex?
complete the square
6 x^2 96 x = 7
x^2  16 x = 7/16
x^2 16 x + 64 = 64 7/16
(x8)^2
vertex at x = 8
Yes, you are right , e. 
Damon
what is f(8)?
6x^2 + 96x + 7 =6(64) +96(8) + 7
= 6(64) +12(64) + 7
= 6(64) + 7
= 391
now you say f(10) is bigger?
6(100) +96(10) + 7
600+960+7
367, nope , disagree
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