3/3, I need the work too. A Box with a square base and open top must have a volu
ID: 2842110 • Letter: 3
Question
3/3, I need the work too.
A Box with a square base and open top must have a volume of 32000 cm3.what are the dimensions of the box that minimize the amount of material used. The graph of a function f is given. Consider the function below when answering the following questions. At what values of x do the local maximum and minimum values of g occur? Where does g attain its absolute extrme (give both X and Y values)? On what intervals is g concave downward and concave down and find all inflection points? Sketch the graph of g.Explanation / Answer
9.
lt the box base side be 'a'.and heoght be h.
we have to minimise f(a,h) = a^2+4ah
constrained to h.a^2 = 32000
=> f(a,h) = a^2 + 4a*(32000/a^2) from abv equation
=> f(a,h) = a^2 + 128000/a = f(a)
f'(a) = 2a-128000/a^2 = 0
=> a = 40 cm =>
h = 20 cm
=> dimensions are 40x40x20
10.
(a)
g has a local min or max when g'(x) = 0
=>
f(x) =0 since g'(x) = f(x)
f(x) =0 at 0, 2s,4s,6s,....
i.e at x=0, 6,12,18,24,......
(b)
g(x) is nothing but the area of the curve f(x) with x-axis, we can see from the figure that area is global maximum when x = 2s , i.e when x = 6
(c)
g''(x) = f'(x)
g is concave upwards when g''(x)> 0 => f'(x)>0 => f is increasing
=> from the figure, the g(x) is concave upwards in following intervals
{(0,s)U(3s, 5s),(7sU9s)U....} i.e {(0,6)U(18,30)U(42,54)U....}
and concave down in remaining intervals i.e.
{(s,3s)U(5s,7s)U.....} i.e {(3,9)U(15,21)U.....}
g(x) has a inflection point when g''(x)=0 => f'(x) = 0
=>
x = s,3s,5s,....
i.e when x = 3,9,15,21,.....
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.