(a) Suppose f:R³ → R² is a function for which and Could f be linear? Why or why not? (b) . that Suppose g: R? → R³ is a linear function, and you know • (8) • (C) - } (8)- 3 and

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: Find the linearization L(x) of the function at a. 9 f(x) = a = 3 - L(x) =

A: We have to find the linearization L(x) of the function at a.  We have, f(x)=9x and a = 3

Q: Suppose g is a continuous DECREASING function on the interval [-3,1].

A: 2. As y is a continous decreasing function on the interval -3, 1

Q: If f (x) >0 and f (x)< 0 for all x over a given part of the domain of a function f, then the graph…

A:

Q: 3 Show that the function f(x) = - 2x + 5x has no relative extreme points. Relative extreme points…

A: Consider the function fx=13x3−2x2+5x Differentiate fx=13x3−2x2+5x with respect to x…

Q: Suppose a tour guide has a bus that holds a maximum of 86 people. Assume his profit (in dollars) for…

A: Solve the following

Q: If f and g are functions of time, and at time t = 3, f equals 8 and is rising at a rate of 3 units…

A: From the question we have  f(3)=8   and  dfdtt=3=3 i.e f'(3)=3 Similarly, g(3)=6   and  dfdtt=3=8…

Q: Find the points of discontinuity of the function f(x)={1−x2,x&lt;0x+2,x≥0 if they exist.

A:

Q: 104v 2 -10 -8 -6 -4 -2 0 4 6 8 10 -2 -4 -6 -8 -10 Match the graph with its function by translating…

A: topic - translation of a function

Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: Is there an unbounded function f:[0,1] →R where it is discontinuous only at a single point in [0,1…

A: f: [0, 1] →R Domain: [0, 1] The function is discontinuous at a single point of the domain.   Let's…

Q: 2-→Find-the-residues of the-function-at-its-poles F1:(2)-(2-z-+3)/(z²-4)1

A: The given complex function is: F1(z)=2z+3z2-4

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

A: The function is given by f(x) =-2x3+6x2-3 To evaluate : The point of local maxima or local minima.

Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: Find the linearization L(x)  of the function f(x)=x^3/4  at x=16

A:

Q: What is the relative maximum value of the function f (x) = 2/x – x?

A: Note: - “Since you have asked multiple questions, we will solve the first question for you. If you…

Q: (B) The function f(x) = x² + x +1 has no fixed point, prove that.

A: Let X be a nonempty set and f : X → X. A point x ∈ X is a fixed point of  f, if f(x) =x.  If no…

Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: Determine all critical points for the function. f(x) = x3 - 12x + 3 x = -2 and x = 2 Ox = -2 O x = 2…

A:

Q: If f (x) = x(x - 2), then the critical points %3D of the function f(x) are

A:

Q: ATTACHED THANKYOU

A: Given that the first term of the AP is a and common difference is d.And the AP is constructed by the…

Q: Find all FIRST and SECOND order critical POINTS for f(x) = (x² +x – 2)'/3

A: fx = x2+x-213f'x = 13x2+x-213-1 . ddxx2+x-2        = ddxx2+ddxx+ddx-23x2+x-223        =…

Q: Consider the function f(x,y) - x-44x- 4y and determine if, at the point (4,0) if the function is a…

A: Note: Since you asked multiple questions I solved one. For solution of other problem please post the…

Q: Suppose you are working with a function f[x, y] and you find that f(¹,0) [x, y] ƒ[1, 0]? Why or why…

A: Given: A function fx,y such that f1,0x,y&lt;0 for all points x,y.   To determine: Whether…

Q: If f : [0, 3] → R is continuous not constant, then its range be a closed, bounded interval?

A: Yes true.

Q: 2 Show that the function f(x) = x-4x + 10x has no relative extreme points. 3X Relative extreme…

A: Given, Function: f(x) = 23x3-4x2+10x Differentiate f(x) with respect to x, we get: f'(x) = df(x)dx…

Q: Show that f is linear of slope m if and only iff(x + h) - f(x) = mh (for all x and h)

A:

Q: 2 Determine the definition of the piecewise linear function shown in each of the graphs. 6. 3 2 -4…

A:

Q: At what points are the functions continuous x+3 y =- 3x, Зх, y = y = (2x – 1)3 х-2 x2 -3x-10'

A: To find the points where following functions are continuous y=1x-2-3xy=x+3x2-3x-10y=2x-113

Q: One of the following is a set of linearly dependent functions on the interval (minus infinity,…

A:

Q: Find the critical points of the function x + 1 f (x) = (5 – x)² -

A:

Q: Determine all the critical points of the function f(x) = 3xe3*

A:

Q: f and g are functions of time, and at time t = 3, f equals 9 and is rising at a rate of 2 units per…

A: It is application of derivative.

Q: Suppose we form the composition of two linear functions f(x) and g(x) with slopes m1 and m2,…

A:

Q: A goldsmith finds that the demand for gold is governed by p(x) = –x² + nx, where z is in (troy)…

A:

Q: One of the following is a set of linearly dependent functions on the

A:

Q: Determine any critical point(s) for the function f(x)=  -3 / x2 - 9

A:

Q: Please

A: The given function is

Q: Find the critical points of the function x + 1 f(x) = (5 – x)2 -

A:

Q: Suppose that f(x, y) = e e-x² - 2y² + x Then the maximum value of f is

A:

Q: Find and classify the critical points of the function f(x, y) = x³ – 10.5æ? – y? + 5 - -

A:

Q: 9. Discuss the continuity of the function x 2 x2,

A:

Q: Compute f(c+h)−f(c) at the indicated point. f(x)=6x2​; c=4

A: Given : Function : f(x) = 6x2   To find : f(c+h)−f(c) at c = 4.

Q: The graph of f​(z​)=16^z passes through the points (−1,x ), (0,x)and (1,x) simplify

A: The equation of the graph is given that: f(z)=16z. So, when it passes through the points (-1,x), it…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

Q: If f:[0, 3] → R is continuous, must its range be a closed interval?

A: If f:[0, 3] → R is continuous, must its range be a closed interval

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.