Question

Find the points on the graph of
f(x)= 12(x + 8) − (x + 8)^3 where the tangent line is horizontal.
(x, f(x))= (smaller x-value)
(x, f(x))=(larger x-value)

Answer 1

so find the derivative, let it equal zero and solve for x.

\[f ' (x) = 12 -3(x+8)^2\]

so \[f '(x) = -3x^2 -48x - 180\]

then solve \[-3(x^2 + 16x + 60) = 0\]

Answer 2

so what is it 6, 10?

Answer 3

so (x+6)(x+10) the solutions are x = -6, -10 so the tangents are horizontal at x = -6 and x = -10

Answer 4

dang, for some reason the stupid homework says its wrong :/