the function f(x)=x^4 - 4x^3 has
a.a local maximum at x=0
b.local minimum at x=0
c.decreasing at x=0
d.increasing at x=0
at x=0 there is a point of inflection and its also a stationary point so in what sense will it increase/decrease at x=0?? although the function is decreasing on either side of x=0 but not at x=0
You've rightly figured that x = 0 is not an extremum, hence eliminated the first two options. If you check in the neighbourhood of x = 0, you'll see that f(0-) is unambiguously positive and f(0+) is unambiguously negative. So, f(x) should be decreasing at x = 0.
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