Find the critical points and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to each critical point. Let f(x) = ;xª + + – 216z There are three critical points. If we call them c, C2, and c3, with c < C2 < C3, then C1 = C2 = and cz = Is fa maximum or minumum at the critical points? At c1, f is ? At c2, f is ? At c3, f is ? These three critical give us four intervals. The left-most interval is and on this interval f is 2 v while f' is ? The next interval (going left to right) is On this interval f is ? v while f' is ? Next is the interval On this interval f is ? v while f' is ? Finally, the right-most interval is On this interval f is ? while f' is ?
Find the critical points and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to each critical point. Let
f(x)=64x4+243x3+−542x2−216xf(x)=64x4+243x3+−542x2−216x
There are three critical points. If we call them c1,c2,c1,c2, and c3c3, with c1<c2<c3c1<c2<c3, then
c1c1 =
c2c2 =
and c3c3 = .
Is ff a maximum or minumum at the critical points?
At c1c1, ff is ? Local Max Local Min Neither
At c2c2, ff is ? Local Max Local Min Neither
At c3c3, ff is ? Local Max Local Min Neither
These three critical give us four intervals.
The left-most interval is , and on this interval ff is ? Increasing Decreasing while f′f′ is ? Positive Negative .
The next interval (going left to right) is . On this interval ff is ? Increasing Decreasing while f′f′ is ? Positive Negative .
Next is the interval . On this interval ff is ? Increasing Decreasing while f′f′ is ? Positive Negative .
Finally, the right-most interval is . On this interval ff is ? Increasing Decreasing while f′f′ is ? Positive Negative .
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