I've gotten somewhere on two of these, but I'm stuck on all three
1) If a stone is thrown vertically upward from the surface of the moon with a velocity of 6 m/s, its height (in meters) after t seconds is h = 6t - 0.83t^2. (Round the answers to two decimal places.)
Part 1: What is the velocity of the stone after 3 s?
I did this, I differentiated and solved.
Part 2 has me confused, though.
(b) What is the velocity of the stone after it has risen 8 m?
Plugging 8 in for h and solving seems like a really messy solution. Am I mistaken here?
2) When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel. F = kR^4
How will a 1% increase in the radius affect the flow of blood?
I substituted some values into the function above and got ~10 but I'm assuming that was incorrect. Do I need to derive it and then take the change in R into F'?
3) y = (2ln(x))/x
Find the tangent line at (1,0) and (exp,2/exp)
I know that I need to differentiate to get the tangent line and then solve for the slope and plug it into point slope equation, but I keep getting the wrong derivative on that one, so any help would be nice.