For the function ?(?) = 2? 3 + 9? 2 − 108? + 30 find the...

For the function ?(?) = 2? 3 + 9? 2 − 108? + 30 find the following (round to the nearest thousandth if needed):

a. Interval(s) where the function is increasing

b. Interval(s) where the function is decreasing

c. Relative maximum and minimum points (x and y values)

d. Inflection point(s) (x and y values)

e. Interval(s) where the function is concave up

f. Interval(s) where the function is concave down

Expert Solution

milcah answered 2 years ago

Given the function f(?) = ?3 − 9?2 + 24? − 2 a) Find the critical...

Given the function f(?) = ?3 − 9?2 + 24? − 2 a) Find the critical numbers and make a sign diagram for the first derivative. b) Find the possible inflection points and make a sign diagram for the second derivative. c) Using the information to sketch the graph of the function and show the local mins and maximums and the inflection points on the graph.

The function given possesses real roots: x^3 – 1.7x^2 + 0.84x – 0·108 Using a precision...

The function given possesses real roots: x^3 – 1.7x^2 + 0.84x – 0·108 Using a precision of 1% of a root, find the estimates of all roots using the secant method. After finding a root, reduce the polynomial using polynomial reduction before finding the next root with the secant method. PLEASE USE MATLAB

Find the point (s) on the surface function ??^2 ?^3 = 3 + 8 + 6...

Find the point (s) on the surface function ??^2 ?^3 = 3 + 8 + 6 that are closest to the origin.

Sketch the graph of the function ?(?)= (2x2-5x+2)/(x+1)2, given the derivatives: ? ′(?) = (9?−9)/(?+1)3 and...

Sketch the graph of the function ?(?)= (2x2-5x+2)/(x+1)2, given the derivatives: ? ′(?) = (9?−9)/(?+1)3 and ? ′′(?) = (36?−18)/(?+1)4 Your sketch should consider the following: ● x- and y-intercepts, if any. ● Horizontal and vertical asymptotes, if any. (Show the computation of any relevant limit.) ● Intervals over which ?(?) is increasing/decreasing. ● Intervals over which ?(?) is concave up/down. ● Relative (local) maximum/minimum points and points of inflection, if any. Identify these clearly on the sketch.

Find the local extrema of the following function. f(x,y)=108+7xy-5x2-6y2

4. [22 pts] For the function ?(?) = 2?5 − 9?4 + 12?3 − 12?2 +...

4. [22 pts] For the function ?(?) = 2?5 − 9?4 + 12?3 − 12?2 + 10? − 3 answer the following: a. [2 pts] Determine whether the function represents a polynomial. Justify your answer. b. [4 pts] Determine whether the function satisfies the Intermediate Value Theorem on the interval [0, 5]. Justify your answer. c. [2 pts] Determine the number (quantity) of complex zeros that the function has, provided the each zero is counted by its multiplicity. d. [4...

Find the derivative of the function. A) f(x)=(2+x^3)^2/3 B) h(t)= (t^4-1)^9(t^3+1)^8 C) y = e4x sin(x)...

Find the derivative of the function. A) f(x)=(2+x^3)^2/3 B) h(t)= (t^4-1)^9(t^3+1)^8 C) y = e4x sin(x) D) y= (x^2+2/x^2-2)^3

5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of...

5. Consider the function f(x) = -x^3 + 2x^2 + 2. (a) Find the domain of the function and all its x and y intercepts. (b) Is the function even or odd or neither? (c) Find the critical points, all local extreme values of f, and the intervals on which f is increasing or decreasing. (d) Find the intervals where f is concave up or concave down and all inflection points. (e) Use the information you have found to sketch...

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

Question