(c) Find the value of x for which f(x) has a global maximum. X = eTextbook and Media (d) Find the value of x for which f(x) has a global minimum.

Q: Find the local minimum and maximum of y= x2/ 3 + x2

A:

Q: Does ƒ(x) = (7 + x)(11 - 3x) 1>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: 2. Find the critical points and determine whether they are a maximum, minimum or neither. y = a° –…

A: In the question we have to find the critical point also max. and min. points.

Q: Suppose f'(x) =x4+x3 – 6x2. Determine the value of x where f has a relative minimum value. A x=0 x=2…

A: Given :  f(x) = x^4+x³-6x²

Q: 10. If the minimum of the function y =x 2-4x+21 occurs at x = 2, what are the coordinates of the…

A: We have to find mimimum point

Q: Indicate the values of the global maximum and global minimum for the function, f(x) = xlnx, as well…

A: f(x)=xln(x)f'(x)=ln(x)+x.1xf'(x)=1+ln(x)now f'(x)=01+ln(x)=0ln(x)=-1x=e-1x=0.3678

Q: Find the local maximum and local minimum in (x,y) notation for the following: y=(2x2-7x)/(2x+5)

A:

Q: Find the absolute maximum and the absolute minimum of f(x,y,z) =x+y+? subject to the constraints g…

A:

Q: What is the absolute maximum and the absolute minimum of the function f(x,y,x) = x2 + y2 + z2,…

A: A detailed solution is given below. We can use Lagrange's multiplier to solve the problem.

Q: Find the values of constants a, b, and c such that the graph ofy = (x2 + a) /(bx + c) has a local…

A:

Q: Find the critical points of f(x) = x* – 4x + 2, and identify each as a local minimum, a local…

A: For the function f(x)=x4-4x3+2, to identify the critical points, we will use second order derivative…

Q: Find the minimum value of x²+y² + z²,

A:

Q: Find the absolute maximum and absolute minimum values of z€

A: This question can be solved using the concept of absolute maximum and absolute minimum.

Q: Suppose f'(x) =x++x³ – 6x². Determine the value of x where f has a relative minimum value.

A:

Q: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

A:

Q: What is the global minimum of the function f (x) = x/2 (x – 4)?

A: Find the critical points and evaluate the given function at critical point.

Q: Suppose f'(x) =xr++x³– 6x². Determine the value of x where f has a relative minimum value.

A: F''(2)  greater then 0

Q: 3. The graph of f(x) = 3(x – 2)² – 6 is a parabola that opens %3D with its vertex at (L, -), and…

A: The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If…

Q: Does x=6 belong to a local maximum or a local minimum? Does x=0 belong to a local maximum or a local…

A: Here we have,  differentiate with respect to x

Q: Find the minimum point for the curve y = x- 4x -1.

A:

Q: 1. The graph of f (x) = 2x3 + x² – 20x + 1 has a relative minimum at

A:

Q: If g'(x) =-3x(x+2), then the graph of g(x) has a relative maximum at what value(s) of x?

A:

Q: Give an example that: the f'(c) 0 but c is not a local maximum or local minimum.

A:

Q: z = x? + xy + y² - y

A:

Q: f(x) = -8x + 1 has a: %3D O maximum neither a minimum or maximum O minimum

A:

Q: Find the local minimum/maximum of y=x³-9x²+ 15x+4 A minimum at x=5, maximum at x=1 B minimum at x=1,…

A: Given that: y=x3-9x2+15x+4

Q: Find constants a and b so that the minimum for the parabola f (x) = x² + ax + b is at the point (4,…

A:

Q: Find the maximum of the function f(x, y) = 4xy – x² + 2y² subject to the constraint a + y = 1. Value…

A:

Q: Suppose f'(x) =x4+x3– 6x2. Determine the value of x where f has a relative minimum value.

A: Explanation of the answer is as follows

Q: Find the minimum value of f (x) = x^x for x > 0.

A:

Q: The minimum value w=_____ occurs when y1=_____ y2=______, and  y3=________

A: To solve the Linear programming problem: minimize: w=14y1+56y2+64y3Such…

Q: Find the minimum of the function f(x, y) = x² + y² – xy subject to the constraint 2æ + 2y = 2. Value…

A: We have to find the minimum of the function fx,y=x2+y2-xy subject to the constraint 2x+2y=2.

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

A:

Q: Find the absolute minimum value on (0,∞​) for f(x)=x − 1/x + 14/x^3.

A:

Q: Given f (x)= (x^2) (e^-x) , find the relative maximum and relative minimum point respectively.

A: We will use derivative to find maximum and minimum value for the function. If f(x) is a function.…

Q: Find the relative minimum and maximum of f(x)=(x+1)/(x^2+x+1).

A:

Q: Determine the extremum points and the values of the maximum and minimum of the function + f(x, y) :…

A: Given:  f(x,y)=xy+yx;   g(x,y)=x2+y2-8=0So,…

Q: If f'(x) = x - 2x´ - x + 2, then ƒ has a relative minimum at x= 2

A:

Q: Use the first- and second-order optimality conditions to find all local minimums of f : x € R² → ¤1…

A: The given problem can be expressed asMinimize f : x1+3x2Subjected to h : x12-5x22+5 Firstly, we will…

Q: Find the value for x for which the graph of y =2e reaches its first minimum value.

A: To find the value for x for which the graph of below equation reaches its first minimum value.…

Q: Find all the critical points of  f(x) = 3x4 - 40x3 + 150x2 and classify each as a relative minimum,…

A: Find f'(x) using exponent rule.

Q: Find the absolute maximum and the absolute minimum of the function f(x,y, z) x² + y² + z², subject…

A:

Q: Find the local minimum/maximum of y=x³ – 9x² + 15x + 4 A minimum at x=5, maximum at x=1 B minimum at…

A: How to find local minimum or maxima: Find the critical point by f'(x) =0 Find f''(x) if f''(x) <…

Q: Use the graph to state the absolute and local maximumand minimum values of the function.

A:

Q: Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4]

A:

Q: What is the local minimum value of the function f(x) = x^3(x + 4)

A: We have the given function as fx=x3x+4 For local maxima/minima, we need to calculate critical point…

Q: Let fx) = x + 2x-8. For what value(s) of x does fx) have a local minimum?

A:

Q: If f'(x) = x³ – 2x² – x + 2, then f has a relative minimum at x

A: f'(x)=x3-2x2-x+2, we have to find relative minimum of f.

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.