Explanation Given: The given equation is f ( R ) = t C R 1 + h C R where R is the prey population density, C is the attack rate constant, h is the handling time for a single prey and t is the optimal foraging time. Proof: Differentiate the given equation with respect to R . f ′ ( R ) = C [ ( t R ′ + R ) ( 1 + h C R ) − h C ( t C R ) ( 1 + h C R ) 2 ] f ′ ( R ) = C [ t R ′ + t h C R R ′ + R + h C R 2 − h t R C 2 ( 1 + h C R ) 2 ] Again differentiate with respect to R . f ″ ( R ) = C [ d 2 t d R 2 ( R + 2 R 2 h C + R 3 h 2 C 2 ) + d t d R 2 ( 1 + h C R ) − 2 t h C ( 1 + h C R ) 3 ] = C ( 1 + h C R ) 3 [ d 2 t d R 2 R ( 1 + 2 R h C + R 2 h 2 C 2 ) + d t d R 2 ( 1 + h

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Chapter 6.4, Problem 51E

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To show: That the curve given is concave down if the given condition d2tdR2R(1+hCR)2+dtdR2(1+hCR)−2thC<0 holds.

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Chapter 6.4, Problem 50E

Chapter 6.4, Problem 52E

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Ch. 6.1 - YOUR TURN 1 Find the absolute extrema of the...Ch. 6.1 - Prob. 2YT Ch. 6.1 - Prob. 1WE Ch. 6.1 - Prob. 2WE Ch. 6.1 - Prob. 1E Ch. 6.1 - Find the locations of any absolute extrema for the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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That the curve given is concave down if the given condition d 2 t d R 2 R ( 1 + h C R ) 2 + d t d R 2 ( 1 + h C R ) − 2 t h C &lt; 0 holds.

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To show: That the curve given is concave down if the given condition d2tdR2R(1+hCR)2+dtdR2(1+hCR)−2thC<0 holds.

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That the curve given is concave down if the given condition d 2 t d R 2 R ( 1 + h C R ) 2 + d t d R 2 ( 1 + h C R ) − 2 t h C < 0 holds.