Question

if f(x) = integral from 0 to x of (sqrt(t^3+1)), what is f'(2)?

Answer 1

recall:

\[F(x)=\int_{0}^{x}f(t)dt\]
\[F'(x)=f(x)\]

Answer 2

so, what is sqrt(t^3+1), when t=2?

Answer 3

+-3 right?

Answer 4

sqrt(9) .... we tend to take the primary outcome, so 3 is fine ... but yes :)

Answer 5

we cant have a slope of 3 and -3 at the same time

Answer 6

so how do you know which one it is for sure?

Answer 7

oh right forgot, so it has to be 3

Answer 8

the sqrt function is only valid for non negative numbers

Answer 9

thx

Answer 10

yep