Maxima and MinimaHard
Question
If f(x) = 
(t - 2)(t - 3) dt for all x ∈ (0, ∞), then
(t - 2)(t - 3) dt for all x ∈ (0, ∞), thenOptions
A.f has a local maximum at x = 2
B.f is decreasing on (2, 3)
C.there exists some c ∈ (0, ∞) such that f″(c) = 0
D.f has a local minimum at x = 3
Solution
f′(x) = ex2 (x - 2)(x - 3)
Clearly, maxima at x = 2, minima at x = 3 and
decreasing in x ∈ (2, 3).
f′(x) = 0 for x = 2 and x = 3
so there exist c ∈(2, 3) for which
f′′(x)
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