Let g(x) = F(x)2 g'(x) = where f(x)>0 for all x. First- and second-derivatives for g are given below: g"(x) = 6 f'(x)² f(x)² – 2f"(x) f(x)³ f(x)6 - 2f'(x) f(x)³ (a) If the function fis decreasing in an interval around x = p, what can you say about the function g? O We cannot determine whether g is increasing or decreasing in an interval around x = p Og is constant in an interval around x = p g is decreasing in an interval around x = p g is zero in an interval around x = p g is increasing in an interval around x = p (b) Suppose the function f is concave down in an interval around x = q. Indicate, if possible, the sign of the following quantities: (i) f'(q) ---Select--- (ii) f"(q) ---Select-- (iii) g"(q) ---Select---

Let g(x) = F(x)2 g'(x) = where f(x)>0 for all x. First- and second-derivatives for g are given below: g"(x) = 6 f'(x)² f(x)² – 2f"(x) f(x)³ f(x)6 - 2f'(x) f(x)³ (a) If the function fis decreasing in an interval around x = p, what can you say about the function g? O We cannot determine whether g is increasing or decreasing in an interval around x = p Og is constant in an interval around x = p g is decreasing in an interval around x = p g is zero in an interval around x = p g is increasing in an interval around x = p (b) Suppose the function f is concave down in an interval around x = q. Indicate, if possible, the sign of the following quantities: (i) f'(q) ---Select--- (ii) f"(q) ---Select-- (iii) g"(q) ---Select---

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 8CR

See similar textbooks