Applications: Differentiation
Differentiation
A water pipeline has to be build which runs from house #V# to cottage #B#. House #V# is located by the side of a straight road and cottage #B# lies across a green area from house #V#. The green area measures #100# by #100# metres. The following illustration visualises the situation:
Installing this pipeline along the road costs #20# euros per metre and installation through the green area costs #80# euros per metre. If we denote the length of the pipeline installed along the road by #l# (distance #VA# in the illustration), we can write the cost #k# of the installation as a function of #l#:
\[ k(l) =20\cdot l+80\cdot \sqrt{l^2-200\cdot l+20000} \]
For what value of #l# are the installation costs minimal? Round your answer to the nearest integer.
| #l=# |
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