Let f(x) be a twice differentiable function (i.e. f(x), f′(x) and f′′(x) are defined for all x), and let a ∈ R (a is a real number). If f′(a) = 0 and f′′(a) > 0, then a is a strict local minimum of f.
(a) Express the second sentence in propositional notation by identifying the parts of the statement (labeling them as p, q, etc.) and giving the form of the proposition.
(b) Express the converse, inverse, and contrapositive of the statement, using propositional logic, and in words. Simplify the expressions as much as possible (e.g. using DeMorgan’s laws).
(c) Negate the statement (i.e. if this theorem were not true, what would we be able to say?)
(d) Suppose that f′(a) = 0 and f′′(a) = 0. What (if anything) does the theorem allow you to conclude
about whether a is a strict local minimum? Explain.
for part a i believe f'(a)=0 is p and f"(a)>0 is q and "a is a strict local minimum of f" would then be r so you could say p^q->r