Question

Given the function f(x)=1/4 x^4 - 3/2 x^2
a. discuss the relative maxima, minima relative
b. determine where f is increasing and where f is decreasing
c. Find the points of inflection.
d. Discuss the concavity

Answer 1

I'll let you do the discussion. You just need to recall that
f' = x^3 - 3x
f" = 3x^2 - 3

f is increasing where f' > 0
f is concave up where f" > 0

f has max/min where f'=0
f has inflection where f" = 0