Your equation is wrong.
If x is the base dimension and y is the height,
V = x^2*y = 36 , so
y = 36/x^2
The amount (area) of material needed is:
A = 2x^2 + 3 x*y
= 2x^2 + 108/x
dA/dx = 0 @ minimum area
4x = 108/x^2
x^3 = 27
x = 3 feet
y = 36/(3^2) = 4 feet
A small dog shelter in the shape of a rectangular solid is to have a square base and an open front. If the volume is to be 36ft^3, find the dimensions for which the amount of material needed is a minimum. V=2x*y
4 answers
I hate calculus
Try to see the beauty of it.
Without calculus, you'd get hit by a car whenever you cross a street. When you step off the curb, you have seen that the approaching car is growing in your field of vision at a rate that indicates it will not arrive at the crosswalk by the time you get to the other side, moving at your known walking speed.
You don't consciously assign values to these variables, but your brain takes care of it for you. When you were small, your parents snatched you back until you learned how to interpret what you saw.
Calculus is such a useful tool, you ought to look forward to mastering the techniques it provides to solve real-life problems.
You don't consciously assign values to these variables, but your brain takes care of it for you. When you were small, your parents snatched you back until you learned how to interpret what you saw.
Calculus is such a useful tool, you ought to look forward to mastering the techniques it provides to solve real-life problems.