GroupHomework #3

a) Fill in the following table with values of NiMvSSJ5RzYiLUkkZXhwR0YlNiNJInhHRiU=, for NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiEiIg==, NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiEiIw==, NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiwkIiIkISIi, NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiLCQiIiQhIiJGLg==, NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiISIjISIi, and NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiISIiRiw=. NiNJInhHNiI=NiMpSSJlRzYiSSJ4R0YlNiMkISIiRiQ=NiMkISIiISIjNiMkISIiISIkNiMkIiIiISIkNiMkIiIiISIjNiMkIiIiISIiUse these to estimate the value of NiMtSSVkaWZmR0kqcHJvdGVjdGVkR0YlNiRJInlHNiJJInhHRig= at NiMvSSJ4RzYiIiIh. b) Fill in the following table with values of NiMvSSJ5RzYiKSIiJkkieEdGJQ==, for NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiEiIg==, NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiEiIw==, NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiwkIiIkISIi, NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiLCQiIiQhIiJGLg==, NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiISIjISIi, and NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiISIiRiw=. NiNJInhHNiI=NiMpIiImSSJ4RzYiNiMkISIiRiQ=NiMkISIiISIjNiMkISIiISIkNiMkIiIiISIkNiMkIiIiISIjNiMkIiIiISIi Use these to estimate the value of NiMtSSVkaWZmR0kqcHJvdGVjdGVkR0YlNiRJInlHNiJJInhHRig= at NiMvSSJ4RzYiIiIh. c) Fill in the following table with values of NiMvSSJ5RzYiKSIjNUkieEdGJQ==, for NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiEiIg==, NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiEiIw==, NiMvSSJ4RzYiLUkmRmxvYXRHSSpwcm90ZWN0ZWRHRig2JCIiIiwkIiIkISIi, NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiLCQiIiQhIiJGLg==, NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiISIjISIi, and NiMvSSJ4RzYiLCQtSSZGbG9hdEdJKnByb3RlY3RlZEdGKTYkIiIiISIiRiw=. NiNJInhHNiI=NiMpIiM1SSJ4RzYiNiMkISIiRiQ=NiMkISIiISIjNiMkISIiISIkNiMkIiIiISIkNiMkIiIiISIjNiMkIiIiISIiUse these to estimate the value of NiMtSSVkaWZmR0kqcHJvdGVjdGVkR0YlNiRJInlHNiJJInhHRig= at NiMvSSJ4RzYiIiIh. d) How are the numbers NiMtSSNsbkc2IjYjSSJlR0Yl, NiMtSSNsbkc2IjYjIiIm and NiMtSSNsbkc2IjYjIiM1 related to your answers in parts (a)-(c).

Suppose that NiMtSSJmRzYiNiNJInhHRiU= is a continuous and differentiable function with a local maximum at 2 and an inflection point at 3. Consider each question separately.a) Is it possible that f (2)=1? If not, explain why not. Justify your answer.b) Is it possible that f '(2)=1? If not, explain why not. Justify your answer.c) Is it possible that f ''(2)=1? If not, explain why not. Justify your answer.d) Is it possible that f (3)=1? If not, explain why not. Justify your answer.e) Is it possible that f '(3)=1? If not, explain why not. Justify your answer.f) Is it possible that f ''(3)=1? If not, explain why not. Justify your answer.

The rate at which a population increases or decreases depends on the size of the population (there are more births in a large city than in a small town). Suppose that the population of fish in a lake follows the differential equation: NiMvLUklZGlmZkdJKnByb3RlY3RlZEdGJjYkSSJQRzYiSSJ0R0YpLCYqJi1JJkZsb2F0R0YmNiQiIiYhIiMiIiJGKEYyRjIiI2whIiI=, where P is the population of fish and t is time.a) Suppose the population of fish is 200. Is the population increasing or decreasing? Explain.b) Suppose that population of fish is 2000. Is the population increasing or decreasing? Explain.Many species have a threshold population, written as NiMmSSJQRzYiNiNJIlRHRiU=, below which the population will decrease and eventually die out an above which the population will increase. c) Determine the threshold population for this population of fish.

Suppose that C(1)=-2 and C '(t) < 3 for all values of t. a) Show that C(2) < 1. b) Show that C(5) < 10.c) Is C(9) < 31? Justify your answer.d) Is C(-5) > -23? Justify your answer.e) Could C(4)=8? Justify your answer.