A factory is 5 km from a straight railway at the perpendicular foot B . Town A lies on the railway with A B = λ km . A connection point P lies on A B with A P = x . Highway freight costs twice railway

Question

A factory is 5 km from a straight railway at the perpendicular foot $B$ . Town $A$ lies on the railway with $A B = λ km$ . A connection point $P$ lies on $A B$ with $A P = x$ . Highway freight costs twice railway freight, so, up to a common factor, total cost is $F (x) = x + 2 25 + (λ - x)^{2}$ for $0 \leq x \leq λ$ . If $λ = 10 km$ , which $x$ maximizes the charge?

Options:

Answer:

D

Solution:

A convex function on [0, 10] attains its maximum at an endpoint. $F (0) = 2125 = 105 > 20 = F (10)$ , so the maximum occurs at $x = 0$ .

TestHub · Accepted Answer

A convex function on [0, 10] attains its maximum at an endpoint. F ( 0 ) = 2 125 ​ = 10 5 ​ > 20 = F ( 10 ) , so the maximum occurs at x = 0 .

Mathematics - Application of Derivative Question with Solution | TestHub

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