Question

Estimate the indicated derivative by any method. (Round your answer to three decimal places.)
s = t − t2; estimate ds/dt
t = 4

Answer 1

*s=t-t^2

Answer 2

what does "estimate" mean? the derivative of \(t-t^2\) is \(1-2t\)

Answer 3

if you plug in 4 you get -7

Answer 4

How did you know t-t^2 is 1-2t?

Answer 5

i guess you didn't get to the part about the "power rule" yet
the derivative of \(t\) is 1, because \(t\) is a line with slope 1
the derivative of \(t^2\) is \(2t\) by the all mighty power rule, but you can get it by hand if you like
it will be a bit of work, but it is easy if you memorize that \[\frac{d}{dx}[x^n]=nx^{n-1}\]

Answer 6

That's extremely helpful. Thanks so much!