f(x)=x^4/4−3x^3+3 a) Determine the intervals on which f is concave up and concave down. f is concave up on: f is concave down on: b) Based on your answer to part (a), determine the inflection points of f. Each point should be entered as an ordered pair (that is, in the form (x,y)). (Separate multiple answers by commas.) c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the x-coordinates. Relative maxima at: (Separate multiple answers by commas.) Relative minima at: (Separate multiple answers by commas.)
NOTE: When using interval notation in WeBWorK, remember that:
You use 'INF' for ∞ and '-INF' for −∞.
And use 'U' for the union symbol.
Enter DNE if an answer does not exist.
f(x)=x^4/4−3x^3+3
a) Determine the intervals on which f is concave up and concave down.
f is concave up on:
f is concave down on:
b) Based on your answer to part (a), determine the inflection points of f. Each point should be entered as an ordered pair (that is, in the form (x,y)).
(Separate multiple answers by commas.)
c) Find the critical numbers of f and use the Second Derivative Test, when possible, to determine the relative extrema. List only the x-coordinates.
Relative
Relative
d) Find the x-value(s) where f′(x) has a
f′ has relative maxima at: (Separate multiple answers by commas.)
f′ has relative minima at: (Separate multiple answers by commas.)
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