Create a function f(x) of at least degree 3 that has at least three terms. For that function, use derivatives to find the following information:

1. The function needs to have at least one maximum or minimum value.

2. Find the domain of f(x)

3. Find the y-intercept f(x)

4. End behavior: Find the limit of the f(x) as x approaches both ∞ and -∞

5. Find the increasing and decreasing interval(s) of f(x)

6. Find the interval(s) of concavity

7. Find any maximum points, minimum points, or points of inflection

8. Graph f(x) to verify that if the above answers are correct or accurate.

Expert Solution

milcah answered 2 years ago

Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given...

Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −5, 1, 2; f(3) = 48 Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −3, −2, 0; f(−4) = 24 Find a polynomial f(x) of degree 3 that has the indicated zeros and satisfies the given condition. −2i, 2i, 5; f(1) = 40 Find the zeros of f(x), and state the multiplicity of each zero. (Order your...

Use the secant Method to find a root for the function: f(x) = x^3 + 2x^2...

Use the secant Method to find a root for the function: f(x) = x^3 + 2x^2 + 10x -20, with x_0 = 2, and x_1 = 1.

For the following exercises, use the information about the graph of a polynomial function to determine the function. Assume the ...The y-intercept is (0, 1). There is no x-intercept. Degree is 4. End behavior: as x → −∞, f(x) → ∞, as x → ∞, f(x) → ∞.

The y-intercept is (0, 1). There is no x-intercept. Degree is 4. End behavior: as x → −∞, f(x) → ∞, as x → ∞, f(x) → ∞.

Find f(x) if f is a linear function that has given properties. f(-1)=1, f(3)=9 f(x)=

Find the Taylor polynomial of degree 2 centered at a = 1 for the function f(x)...

Find the Taylor polynomial of degree 2 centered at a = 1 for the function f(x) = e^(2x) . Use Taylor’s Inequality to estimate the accuracy of the approximation e^(2x) ≈ T2(x) when 0.7 ≤ x ≤ 1.3

Let f(x) = ln(x^2 + 9) Find the first two derivatives of f . Find the...

Let f(x) = ln(x^2 + 9) Find the first two derivatives of f . Find the critical numbers of f . Find the intervals where f is increasing and decreasing. Determine if the critical numbers of f correspond with local maximums or local minimums. Find the intervals where f is concave up and concave down. Find any inflection points of f

For the following exercises, use the information about the graph of a polynomial .. The y-intercept is (0, 9). The x-intercepts are (−3, 0), (3, 0). Degree is 2. End behavior: as x → −∞, f(x) → −∞, as x → ∞, f(x) → −∞.

For the following exercises, use the information about the graph of a polynomial function to determine the function. Assume the leading coefficient is 1 or −1. There may be more than one correct answer.The y-intercept is (0, 9). The x-intercepts are (−3, 0), (3, 0). Degree is 2. End behavior: as x → −∞, f(x) → −∞, as x → ∞, f(x) → −∞.

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

For the function f(x) = x(x+1) find the exact formula for f′(x). Use only the definition...

For the function f(x) = x(x+1) find the exact formula for f′(x). Use only the definition of the derivative.

Question