In: Math
Please evaluate these question with every step and every explanation for each of one.
Lef f(x)= -(3/8)x4+x3+1, where x∈(−∞,∞)
1)Find the critical numbers of f(x)
2)Find the absolute maximum value and the absolute minimum value of f(x) on the closed interval [-1,3]
3)Find the intervals where f(x) is increasing and the intervals where it is decreasing. Find the local maximum values and the local minimum values of f(x)
4)Find the intervals where the graph of f(x) is concave upward and the intervals where it is concave downward. Find the inflection points of f(x)