Question

In: Math

1. You are given the function f(x) = 3x^4 + 4x^3 a) Find the x and...

1. You are given the function f(x) = 3x^4 + 4x^3

a) Find the x and y- intercepts.

b) Find the critical number(s) of f.

c) Find the interval(s) of increase and decrease of f.

d) Find the relative maximum and minimum value(s) of f.

e) Find the hypercritical number(s) of f.

f) Find the interval(s) of upward and downward concavity of f.

g) Find the point(s) of inflection of f.

h) Sketch the graph of f.

2. You are given the function f(x) = x/(1−x)

a) Find the x and y- intercepts.

b) Find the horizontal asymptote(s).

c) Find the vertical asymptote(s) and do a limit analysis of the behavior of f on either
side of each vertical asymptote.

d) Find the critical number(s) of f.

e) Find the interval(s) of increase and decrease of f.

f) Find the relative maximum and minimum value(s) of f.

g) Find the hypercritical number(s) of f.

h) Find the interval(s) of upward and downward concavity of f.

I) Find the point(s) of inflection of f.

j) Sketch the graph of f.

3. Find the absolute maximum and absolute minimum of f(x) = x^3 − 3x on [0, 3].

4. Why doesn’t the Extreme Value Theorem apply to f(x) =1/x on the interval [-3, 3]?

Expert Solution

milcah answered 2 years ago

Given f(x) = x^4 - 4x^3 1) find the intervals on which f is increasing or...

Given f(x) = x^4 - 4x^3 1) find the intervals on which f is increasing or decreasing. 2) find the local maximum and minimum values of f. 3) find the intervals of concavity and the inflection points

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which...

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which f is increasing/decreasing and identify any local extrema. (b) Find the intervals on which f is concave up/down and find any inflection points. B. Consider the function f(x) = sin(x) + cos(x). Find the absolute minimum and absolute maximum on the interval [−π,π].

For the function f(x)=x^4-3x^3+x^2+4x+21 Use long division to determine whether x+3 is a factor of f(x)....

For the function f(x)=x^4-3x^3+x^2+4x+21 Use long division to determine whether x+3 is a factor of f(x). Is x+3 a factor of f(x)?

Consider the function f(x) = 3/(3x+ 4), c= 0 a)Find the power series for the function...

Consider the function f(x) = 3/(3x+ 4), c= 0 a)Find the power series for the function centered at c b)Determine the interval of convergence

Question1: Find the interval of increase and decrease of given function f(x)=3x^5-5x^3 f(x)=1/3 x^3-9x+2

use the given zero to find the remaining zeros of each polynomial function 23. f(x)=x^3-4x^2+4x-16; zero;...

use the given zero to find the remaining zeros of each polynomial function 23. f(x)=x^3-4x^2+4x-16; zero; 2i 27. x^4-9x^3+21x^2+21x-130; zero: 3-2i Find the complex zeroes of each polynomial function. Write f in factored form. 35. f(x)=x^4+5x^2+4 I tried using Descarte's rule for questions 23 and 27, but I don't what to do after that. Also, after you explain the steps I need to solve the question, could you help understand why these steps are necessary?

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals where f is positive and where f is negative. Does f have any horizontal or vertical asymptotes. If so, find them, and show your supporting calculations. If not, briefly explain why not. Compute f′ and use it to determine the intervals where f is increasing and the intervals where f is decreasing. Find the coordinates of the local extrema of f Make a rough...

a) Let f(x) = −x^4 − 4x^3 . (i) Find the intervals of increase/decrease of f....

a) Let f(x) = −x^4 − 4x^3 . (i) Find the intervals of increase/decrease of f. (ii) Find the local extrema of f (values and locations). (iii) Determine the intervals of concavity. (iv) Find the location of the inflection points of f. (v) Sketch the graph of f. (You can choose your own scale for the graph) b) A farmer wants to fence in an area of 6 km2 in a rectangular field and then divide it in half with...

Given f''(x)= 4x-6 and f'(-2)=5 and f(-2)=1 FIND: Find f'(x)= and find f(2)=

Let f(x) = −x^4 − 4x^3. (i) Find the intervals of increase/decrease of f. (ii) Find...

Let f(x) = −x^4 − 4x^3. (i) Find the intervals of increase/decrease of f. (ii) Find the local extrema of f (values and locations). (iii) Determine the intervals of concavity. (iv) Find the location of the inflection points of f. (v) Sketch the graph of f. (You can choose your own scale for the graph)