Puzzle 1
An university student works from 7 p.m. to 11 p.m. assembling mechanical components.
The cummulative number N of components assembled after working t hours is determined by the function

N(t) = - 0.093t3 + 0.65t2 + 7.81t,

where 0 ≤ t ≤ 4. At what time is student assemblig components at the greatest rate?

Puzzle 2
The deflection
D of a particular beam of length l is given by

D(x) = 2x4 - 5L x3 + 3L2x2

where x is is the distance from one end of the beam.
Find the value of
x that yields the maximum deflection.