Let f(x)=−x^4−8^x3+5^x+2. Find the open intervals on which f is concave up (down). Then determine the x-coordinates of all inflection points of f.

Question

1. f is concave up on the intervals
2. f is concave down on the intervals
3. The inflection points occur at x =

Answer 1

Did you reall mean 5^x, or 5x^2? I will assume the latter. Since

f" = -12x^2-48x+10

and that has two roots, those are where the inflection points lie.