# Find the maximal and minimal by derivatives

Not what you're looking for? Search our solutions OR ask your own Custom question.

Please help me with the following calculus problem:

1. A homeowner wants to enclose a 5,800 square feet rectangular garden by a fence in his backyard. If three sides of the fence cost $6.25 per foot and 4th side costs $10.25 per foot, find the dimensions that will minimize the cost of building the fence and the minimum cost of its construction.

2. Find the absolute extreme values of f(x) = x^4 + 8x^3 - 32x^2 on interval [-1, 5].

Â© BrainMass Inc. brainmass.com March 5, 2021, 12:05 am ad1c9bdddfhttps://brainmass.com/math/derivatives/finding-maximal-minimal-derivatives-480124

#### Solution Preview

1. Suppose the length is x feet, width is y feet.

we could have xy=5800.

cost z=6.25*(2x+y)+10.25y

z=12.5*5800/y+16.5y=72500/y+16.5y

z'=-72500/y^2+16.5.

when z'=0, y=66.29 ...

#### Solution Summary

The solution provides detailed explanation how to find the maximal and minimal by derivatives.

$2.49