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.