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Solution to the problem of the (previous) week
Problem:The shaded triangle is bounded by the axis as well as the tangent and normal lines of the graph of the function at the point
Determine and in terms of the coordinate of For which is the area of the triangle minimal, and what is the minimum value
(The results should be correct to four decimal places.)
Solution:At the point the slope of the tangent line is and the slope of the normal line is .
The area of the shaded triangle is
Since as or we obtain the corresponding minimal area