Question

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?

Answer 1

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
(x-8)^2
vertex at x = 8
Yes, you are right , e.

Answer 2

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