Consider the function below. (If an answer does not exist, enter DNE.) g(x) = 150 + 8x³ + x4 (a) Find the interval of increase. (Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value(s). (Enter your answers as a comma-separated list.) Find the local maximum value(s). (Enter your answers as a comma-separated list.) (c) Find the inflection points. (х, у) %3 (smaller x-value) (х, у) - (larger x-value) Find the interval where the graph is concave upward. (Enter your answer using interval notation.) Find the interval where the graph is concave downward. (Enter your answer using interval notation.)

Q: e2x-1 At what x-value(s) does f(x) = have relative maximum ? %3D x2

A: We know that  For relative maximum  We Find the first derivative of a function f(x) and find the…

Q: Consider the function f(x) = 1 – 7x2, - 5 <a < 2. The absolute maximum value is and this occurs at a…

A:

Q: Does ƒ(x) = (7 + x)(11 - 3x) 1&gt;3 have an absolute minimum value or an absolute maximum?

A: Here we have,  f(x)=(7+x)(11-3x)13 differentiate with respect to x

Q: find a so that f (x) = ax2 + 8x -8 has a minimum value of -24

A: According to the given information, it is required to find the value of a so, that the function f(x)…

Q: Q1- Find any local maximum and local minimum values and sketch the curve: x? + 1 f(x) x2 – 1

A: Sketching curve and finding extremums.

Q: What is the absolute minimum value of the function f(x) = x' - 3x² on the interval [-2, 4] ? a. -4 O…

A:

Q: (a)Find the inflection point(s) and (b) local minimum and maximun f(x)=x4-50x2+6

A: forcriticalpoints.

Q: nd the absolute maximum value and the absolute minimum value, if any, of the given function. (If an…

A:

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A:

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A:

Q: Given F(x)= (5)/(x^(2)+1)+2 , find the local minimum and local maximum values if they exist, then…

A:

Q: For what value of x does the function f(x) =x³ 4x attain the absolute minimum %3D in the interval…

A:

Q: Sketch the graph of g(x), identify the absolute maximum, the absolute minimum, the local maximum and…

A:

Q: 10. Given that f is a quadratic function with minimum f(3) = 6, find the vertex, range, and…

A: Consider the given question,Quadratic equation is a parabolic equation and its vertex is highest or…

Q: Consider the function f(x) = 1 – 6x?, - 3 < x < 1. The absolute maximum value is and this occurs at…

A:

Q: At which value does the function g(x)= 3x^4 - 4x^3 attain a minimum and what is the minimum value?…

A: Sol:- Suppose that x=c is a critical point of fx then, If f 'x&lt;0 to the left of x=c and f 'x&gt;…

Q: Does the function f(x, y) 2 + 6y3 + 5y? – 4x have a global maximum and global minimum? If it does,…

A: Let us first evaluate the partial derivatives of the given function as shown below:…

Q: 22. Find the maximum or the minimum value of f(x)=-2x² –10x+5. SLO 11

A: To find the maximum and minimum values of the function

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A:

Q: Does the function f(x, y) = + 8y" + 2y² – 5æ have a global maximum and global minimum? If it does,…

A: given function fx,y=x22+8y3+2y2-5x claim- to check whether the function have a global maximum and…

Q: Enter the function f (x)= x2-2x-8 in the form f (x) = a(x-h)? +k, where a, h, and k are constants.…

A:

Q: 14. Find the minimum value of the function f(r) = x + 4x + 5. -2 5 1.

A: Given function: fx=x2+4x+5 To determine: Minimum value of the function.

Q: What is the minimum of the function y = -a + 3x for a <-1? %3D -4 -2 04 O2

A:

Q: 3x²-by?-9x ニ Local maximum valuels) = ? Local minimum valuecs)= ? Suddle point(s) こ (xy.f) = ?

A:

Q: Consider the function f(x)=x^4−72x^2+9, -5≤x≤13. This function has an absolute minimum value  =?…

A: f(x)=x4−72x2+9f'(x)=4x3-72(2x)+0f'(x)=4x3-144xFor the critical numbers…

Q: Consider the function  f(x) = xe-8x,   0</= x </= 2. this function has and absolute minimum value…

A: Given function is f(x)=xe-8x, 0≤x≤2 Differentiate f(x) with respect to x.…

Q: 10 10 f(x) = 3x - x³

A: The function of the curve on the graph is: fx=3x2-x3

Q: z = x? + xy + y² - y

A:

Q: For what value of x does the function f(x) - 4x attain the absolute minimum %3D in the interval…

A: The given function is                                        f(x)=13x3-4x and the given interval is…

Q: Find the absolute maximum value and the absolute minimum value, if any, of the given function. (If…

A:

Q: Find the absolute maximum and absolute minimum y-values of the function f(x)= -7 - 5x - 11/x on the…

A:

Q: 1) is it a convex function or a concave function? Explain 'why' in terms of the given equation.  2)…

A:

Q: Where does the minimum or maximum value occur? X =

A:

Q: Given that a function y=x3, has a vertex at (-2,0), a local maximum at (-1,3), and a local minimum…

A: Given that a function y=x3, has a vertex at -2,0, a local maximum at -1,3, a local minimum at -3,-3,…

Q: Consider the function f(x) = 1 – 3x2, - 5 < x < 2. %3D The absolute maximum value is and this occurs…

A:

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = 2x3 - 6x² -18x (a) Find the…

A:

Q: Find the minimum value of the function f(x) = x – 10x. - Nood

A:

Q: Use the function’s equation .f(x) = 2x2 + 12x + 703, and not its graph,to finda. the minimum or…

A: Given function is fx=2x2+12x+703. We know that if fx=ax2+bx+c then maximum or minimum value occurs…

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A: To find the absolute maximum and absolute minimum of f(x) on [0,2].

Q: Consider the function below. B(x) = 3x2/3 - x (a) Find the interval of increase. (Enter your answer…

A:

Q: Draw the graph of f ( x ) =3 x2+5 x−4 for a. From the graph, identify the values of x when f (x)=0.…

A: Follow the steps below to plot the graph of y=f(x) . Take arbitrary integers for the values of x…

Q: Use calculus to find the absolute maximum and the absolute minimum values of the function g ( x ) =…

A: The given function on the interval is [-2, 2]

Q: Consider the function f(x) = 5 – 3x², – 5 < x < 1. The absolute maximum value is and this occurs at…

A: The given function is: f(x)=5-3x2,            -5≤x≤1

Q: Consider the function f(x) = 2 – 7x², - 4 <x < 2. The absolute maximum value is and this occurs at x…

A:

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A:

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A: For the given function f(x)=-x2+4x+3. taking first derivative with respect to x,…

Q: Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an…

A: Given:fx=12x4-23x3-2x2+3  on  -3,3Absolute extrema:1. Check to make sure f is continuous over…

Q: Find all values of x, if any, where the function f(x) = x° – 5x³ – 20x – 2 has local maximum and…

A:

Q: Does the function f(*,2) = + 5y3 have a global maximum and global minimum? If it does, identify the…

A:

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.