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!

Question

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!

amistre64 · Answer

increaseing or decreasing is a 2nd derivative test... not a 1st derivative test :)

anonymous · Answer

No...don't think so

amistre64 · Answer

A' = 5t^4 -20t^3 +60t^2

A' = 5t^2(t^2 -4t +12) = 0

amistre64 · Answer

12..6.2

(t-6) (t+2)

t = 6, -2, and 0 are your crits

amistre64 · Answer

what were you having issues with?

amistre64 · Answer

slope is a function of the 1st derivative; concavity is a function of the 2nd derivative

anonymous · Answer

6 x -2 is -12, not +12

amistre64 · Answer

hmmm.... you might be right :)

amistre64 · Answer

my eyes were deceiving me... ;)

amistre64 · Answer

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

anonymous · Answer

Right. Thanks!