The table of values represents a polynomial function f(x). How much greater is the average rate of change over the interval (7, 9] than the interval [4, 6 ? Enter your answer in the box.

Q: -4x By use of the product rule, differentiate the function f (x) = x³e¬4×.

A: Rule:

Q: Find the zeros of the function f(x) = (x + 3)/(2x2 − 6)algebraically.

A: To Determine: Find the zeros of the function algebraically. Given: we have a rational function…

Q: The function C(x)=10x+5,000 represents the cost to produce x number of items. How many items should…

A: SOLUTION-

Q: Find the y-intercept of the polynomial function. f(x) = x2(x - 1)(x - 6)

A: Find the y-intercept of the polynomial function.f(x) = x2(x - 1)(x - 6)

Q: Find the value of b that gives the function the maximum value of 19. f(x)=-x^2+bx+3

A: At the point of maximum the first derivative of the function becomes zero and the second derivative…

Q: 3. Sketch the graph of the polynomial function. Make sure to label the roots and y-intercept (g) 1(r…

A: see below the answer y-intercept is calculate y when x=0 And the y=intercept and roots of the…

Q: Use the graph to write the formula for a polynomial function of least degree f(x) = f(x) 2 -4 12 4…

A: From given graph  zeros x1=-2,x2=1,X3=3

Q: At a manufacturing plant, the total cost to produce x items is given by the function c(x)=…

A: Consider the provided information, the total cost that produces x items is defined as,

Q: 4. Given the function y = (3 - 2x²)/(1- x -2x?), (a) Find the difference quotient Ду/Дх.

A: Topic:- Difference quotient

Q: The heights of two different projectiles after they are launched are modeled by the f(x) and g(x).…

A: Given, The function f(x) is defined as: fx=-16x2+55x+19 The quadratic function g(x) values are shown…

Q: Use the graph to write the formula for a polynomial function of least degree. f(x) f(x) 4 2 - x -4…

A: First see the numbers zeros of the polynomial than write the equation in the following of zeros of…

Q: f (x) = Vx² – 4.

A:

Q: 3. Sketch the graph of the polynomial function. Make sure to label the roots and y-intercept (G)…

A:

Q: Determine the domain and range of the quadratic function.   f(x)=−4(x+1)^2 − 4   Enter your…

A: We have to find the domain of :  f(x)=−4(x+1)2 − 4.

Q: The slope of the function f(x) : –2x+3y= 6

A:

Q: 2. Determine whether each function is a polynomial function or another type of function. Justify…

A:

Q: Find the point of inflection and concave of the graph of the function. (If an answer does not exist,…

A:

Q: Find the zeros of the function f(x) = 3x + 18 algebraically.

A: Given;            fx=3x+18 Solve for x:          3x+18=0

Q: For what x does the function g(x) = 10 + 40x - x2 have its maximum value?

A:

Q: Find the point at which the line f(x)=5x+14 intersects the line g(x)=−2x (_,_)

A: Given that,  Line f(x) =5x+14 and line g(x) = -2x intersects. So, both the function gives the same…

Q: 1. Which of the following equations is not a polynomial function? Justify your answer. i. y =-x+ 5…

A:

Q: Find the zeros of the function. g(z) = 7z2 +21

A:

Q: Find the zeros of the function f(x) = 5x² – 13x – 6

A: Let us consider the function ax2+bx+c =0 Then   x =-b±(b)2-4ac2a

Q: for what value of x does the function g(x)=1/3x3-2x2 attain the point of inflexion?

A:

Q: State whether the function is a polynomial function or not. If it is, give its degree. If it is not,…

A: A polynomial is an expression that can be built from constants and symbols called variables or…

Q: 2. Match each graph of a polynomial function with the corresponding equation. Justify your choice. 3…

A: Given: f(x)=-2x3+7x+1

Q: Find the point at which the line f(x)=-3x+1 intersects the line g(x)=3x+7

A:

Q: 2) Find the domain of the function. 7- 4x f (x) = 3x + 2

A:

Q: the zeros  of a cubic function are -1,-2/3,and 5. what are all the factors of (x).

A:

Q: For what value of x will the function f(x) = -3(x - 10)(x - 4) have a maximum value? Find the…

A:

Q: Find the zeros of the function algebraically. <2 – 17x + 72 f(x) = 3x

A:

Q: Find the domain of the function f(x)=17x+3f(x)=17x+3. What is the only value of x not in the…

A: the function given to us is  f(x) = 17x + 3

Q: Find the domain of f(x) = v- 4x + 8

A: The domain or set of departure of a function is the set into which all of the input of the function…

Q: Find the y-coordinate of the y-intercept of the polynomial function defined below. f(x) = (x + 3)…

A:

Q: Find the local extrema of the functionf(x)=x2 / x4+16.

A:

Q: Why f(x) = - is not a polynomial function? %3D M 2х

A: In a polynomial function, exponent of the variable should not be fraction, radical or negative.

Q: What number of rooms filled produces the maximum revenue?

A: Differentiate the given revenue function and quate it in to zero then solve for x. The. We get the…

Q: The length of a rectangle is 7 inches less than twice the width, w, of the rectangle. The quadratic…

A: Given , The length of a rectangle is 7 inches less than twice the width, w, of the rectangle The…

Q: Find the sum of the polynomial functions. (Simplify your answer completely.) P(x) = 5x4 − 4x + 4…

A: Given,

Q: Determine whether the function y = -3x2is increasing or decreasinga. For x &lt; 0. b. For x &gt; 0.

A: Given, y=-3x2Differentiating both sides w.r.t x we get:dydx=ddx(-3x2)⇒dydx=-6x…

Q: Which of the following is a polynomial function? A (x)-x+2x +4 B. (x) x + 2/x-2 C f) Vy - 2()+5(V)-…

A: “Since you have posted a multiple question, we will solve the first question for you. To get…

Q: Find all zeros for the function f(x) = x4 - 8a3 + 3x2 + 40x - 12

A: Here we use quadratic formula. For quadratic equation ax2+bx+c =0 Then x =-b ±(b)²-4ac2a

Q: a) explain why f (x) = x²-1 s not a polynomial function ? x+5

A:

Q: What is the formula for w(x), the node polynomial?

A: Node Polynomial: Let f (X) be a function on the interval [a, b] and n nodes are chosen on the…

Q: Find the point at which the line f(x)3 4x6 intersects the line g(x) =-4 +2

A:

Q: Find f(-2) for the function f(x) = 3x2 – 2x + 7. 2 -13 B -1 1 23

A:

Q: A soft-drink vendor at a popular beach analyzes his sales records and finds that if he sells cans of…

A: Given: P(x)=-0.001x2+3x-1800

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.