The inflection point of f(x)= -2(x-4)^3 +11 is where f''(x) = 0.
f'(x) = -6(x-4)^2
f''(x) = -12(x-4)
f''(4) = 0, so the inflection point occurs when x = 4
f(4) = 11, so the inflection point is (4,11)
End Behavior is what happens when |x| → ∞
You learned in algebra 2 and/or precalculus that the End Behavior of the graph of a polynomial function depends on whether its degree is even or odd and the sign of its leading coefficient.
If the leading coefficient is positive then the right side end behavior is up; if the leading coefficient is negative then the right side end behavior is down. Test this with x = 10^100.
The left side end behavior is the same as the right side for even degree polynomial functions and opposite for odd. Test this with x = -10^100.
f(x) has a negative leading coefficient, so its right side end behavior will be down. f(x) is an odd (3rd) degree polynomial function so its left side end behavior will be opposite to its right side, i.e., up.