Consider f(x)=200+8x^3+x^4. find the intervals on which function is increasing or decreasing, the local max and minimu values, the intervals of concavity and the inflection points

Answer 1

Increasing where f' > 0
Decreasing where f' < 0

f'(x) = 24x^2 + 4x^3 = 4x^2(6+x)

Concave up where f'' > 0
Concave down where f'' < 0

f'' = 48x - 12x^2 = 12x(4-x)

Max where f' = 0 and f'' < 0
Min where f' = 0 and f'' > 0