Water is poured into a container that has a leak. The mass m of the water is given as a function of time t by m = 4.9t.8 - 3.0t + 21, with t ≥ 0, m in grams, and t in seconds.(a) At what time is the water mass greatest, and (b) what is that greatest mass? What is the rate of mass change at (c) t = 2.4 s and (d) t = 5.4 s?
I know that part c and d have to kg/min
The Attempt at a Solution
I got part (a) correct as 3.80911 by finding the points of inflection from the derivatives and then looking at where the equation changes from positive to negative. Part (b) was also easy because all I had to do is plug my answer into the original equation and I got 23.8568361. It's part (c) and (d) that I'm having trouble with.
For part (c) and (d) I know I have to take the derivative so I did and got
3.92t-.2 - 3.0 then I plug in
3.92(2.4)-.2 - 3.0=.2903630437g and 3.92(5.4)^(-.2) - 3.0= -.2022602387g