Here's the question you clicked on:
mathcalculus
find the critical points: s(t)= (t-1)^4 (t+5)^3
i found the derivative. 4(t-1)^3 3(t+5)^2
is it just \[(t-1)^4(t+5)^2\] ?
with the chain rule those are not the derivatives...
yes but instead of 2 as an exponent its 3. i know im suppose to = 0 then im not sure what to do.
wait that is right, t is single power, sorry.
okay so i did it wrong can we review step by step
just to be clear, it isnt the two equations plus one another, its them two multiplied by one another?
so i get.... 4(t-1)^3 3(t+5)^2
(t-1)^3 (t+5)^2 (17+7 t)
I'm trying to figure that out, I used Wolframalpha to check my work and it got something different.
Use the product rule!!! \[\huge s(t)= (t-1)^4 (t+5)^3\] \[\huge s'(t)=4(t-1)^3(t+5)^3+3(t+5)^2(t-1)^4\] \[\huge =(t-1)^3(t+5)^2[4t+20+3t-3]\] \[\huge =(t-1)^3(t+5)^2(7t+17)\] At S.P's s'(t)=0 \[\huge (t-1)^3(t+5)^2(7t+17)=0\] \[\huge t=1, t=-5, t=-\frac{17}{7}\]
\[s(t)=y\] To find the values of y, sub in the values of t into the original equation.
Don't think you need to describe the nature of the curve [ie. Maximum or minimum turning point, etc.]. But I think you still need to find the inflection points of the function.
how did you get to this step: =(t−1)3(t+5)2[4t+20+3t−3]