Find the intervals in which the function is increasing and decreasing. Also, find and classify all the critical points of the function using the First Derivative Test. A(t)=t^5-5t^4+20t^3-17 I am having trouble setting the derivative equal to zero. Please help!

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Find the intervals in which the function is increasing and decreasing. Also, find and classify all the critical points of the function using the First Derivative Test. A(t)=t^5-5t^4+20t^3-17 I am having trouble setting the derivative equal to zero. Please help!

Mathematics
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increaseing or decreasing is a 2nd derivative test... not a 1st derivative test :)
No...don't think so
A' = 5t^4 -20t^3 +60t^2 A' = 5t^2(t^2 -4t +12) = 0

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12..6.2 (t-6) (t+2) t = 6, -2, and 0 are your crits
what were you having issues with?
slope is a function of the 1st derivative; concavity is a function of the 2nd derivative
6 x -2 is -12, not +12
hmmm.... you might be right :)
my eyes were deceiving me... ;)
if its got imaginary roots, then we probably dont need to both with it.... right? sqrt(16 - 48) = sqrt(-32) no "real" roots for this, go with t=0 as the critical, and it probably an inflection point
Right. Thanks!

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