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

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

11th Edition

ISBN: 9780133886832

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 6.4, Problem 51E

To determine

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.4, Problem 50E

Chapter 6.4, Problem 52E

Students have asked these similar questions

the correct answer is Ccould you please show me how to do it using the residue theorem

Use the information to find and compare Δy and dy. (Round your answers to four decimal places.) y = x4 + 7 x = −3 Δx = dx = 0.01 Δy = dy =

4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown in the table. For each problem, approximate the distance the car traveled (in miles) using the given method, on the provided interval, and with the given number of rectangles or trapezoids, n. Time (min) 0 6 12 18|24|30|36|42|48|54|60 Speed (mph) 0 10 20 40 60 50 40 30 40 40 65 a.) Left Rectangles, [0, 30] n=5 b.) Right Rectangles, [24, 42] n=3 c.) Midpoint Rectangles, [24, 60] n=3 d.) Trapezoids, [0, 24] n=4

Chapter 6 Solutions

Calculus with Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Lial, Greenwell & Ritchey, The Applied Calculus & Finite Math Series)

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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.

Videos

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

Want to see the full answer?

Chapter 6 Solutions

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.