Let f(x) = 1+ V7x +1. Determine the largest possible domain of f(x) Select one: • [-1/7, +o0)

Q: Find the limit of f(x) = √(4 − x2) as x approaches −2 from the right.

A: We will find the limit by substitution

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: For the continuous function f(x), if f’(-4) does not exist, then x=-4 is a critical point.

A:

Q: Find the antiderivative F of f(x)=4-3(1+x^2)^-1 that satisfies F(1)=-2.

A:

Q: Find the funchion f Such that F(x) xf (x)-x and fo) 2

A: Convert the given problem to a simple differential equation and solve the same.

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: Find the global maximum of f(x) = x(4−2x) over the interval (−∞,∞)

A: Given:The function is f(x) = x(4-2x) .The interval is (−∞, ∞).

Q: Find the critical numbers of the function f(z) = z2 - z / Answer (separate by commas): z =

A: Solve the given problem.

Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)

A:

Q: Define the function f(x, v) = 4x³-x³y-4y5 3x5-3y5 at the origin so that it becomes continuous there.

A: A function is said to be continuous at (a,b) if the the value of function at (a,b) is equal to…

Q: on f(x, y) = 3x + 9y subject to th %3D

A:

Q: f(x) = z²+6x+5 x-1

A: On solving this we will get

Q: Find linearization L(x) of f (x) = Vx at a =4 and use to approximate 7.8.

A:

Q: Find the constant a such that the function is continuous on the entire real line. S 8x², f(x) ax -…

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Q: Find the minimum and maximum of the function in the specified interval. 1. f(x) = x² - 6x + 9 on…

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Q: Find the limit of f(x) = v9 – x² as x approaches -3 from the right.

A: follow next step

Q: Find the interpolating polynomial of degree two for f(x) cos(r2) +r on the interval [-1, 1] using…

A:

Q: Let f(r) = 1-5r2. Use the limit definition of the derivative to show that f'(z) = -10r. %3D

A:

Q: differentiate the follouwing 243 a) f(x)=2x°-in/x|+3 arccos (X)

A: Since you have asked multiple questions in the same request, as per the policy, only the first…

Q: Show that the function f : [0, 1] →[0, 1] given by f(x) = (x −1)2 has a fixed point. Can you apply…

A:

Q: Integrate f(x) from x = 0 to 10 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000+24563x -…

A: Given f(x)=5000+24563x-7418x2+768x3-31x4+0.14x5 Let I=∫010f(x)dx Here a=0 and b=10

Q: For f(z) = 2z', find ip using the definition,

A: The limit definition of a derivative of a function, f(x) at a point, x=a is given by .

Q: Let f(z) (x-iy)e- ) Determine the points at which exist, and find r(2) at these points.

A:

Q: Find the best quadratic approximation to f on the interval [ 0, 1].                     f(x) = x3

A:

Q: Vhat is the largest output value of the function z = 2x + 2y that can be obtained by plugging in…

A: In this question, the value of the function is checked at the corner point. The maximum value of the…

Q: Determine whether the function 2х + 1 f(x) %3D 2r2 2x2 – x – 1 is continuous: a. at 2; b. at 1.

A:

Q: Find the best quadratic approximation to f on the interval [ -1, 1].                     f(x) = lxl

A:

Q: Prove that f(x) = other than the graphing method. x² – 1 is continuous at c = 0 by any method |

A:

Q: Find the constant c that makes g continuous on (-0;0) x-2x-8 g(x) = a+1 if x+2 if X=-2

A: Continuity of a function at a point x=c : If function is defined at x=c and limx→c fx=fc then we can…

Q: what is the antiderivative F(x) of f(X) = 3x1/2-x-1 that satisfies the condition  F(4)= 0? A,…

A: The given function is fx=3x12-x-1 that satisfies the condition F4=0. Find the antiderivative of Fx.

Q: Let 'f be a continuously differentiable real valued function defined bx+a x<1 by f(x) = 5x² Then the…

A:

Q: Determine f such that f′′(x) = 12x − 1 and 1 is both a critical number and a y- intercept of f

A: Given:  and 1 is both critical number and y-intercept.

Q: 24, Find the domain of H function fw =J 2x+3 -1

A: Given,

Q: Determine the maximum value of f (x) = 5x – e5x [T:3] on the interval [-1,1] %3D

A:

Q: Find the limit of the function f(x) = x²esin(1/x) as x approaches to zero.

A: To find limit of function f(x)=x2esin(1/x) as x approaches to 0. (Using Squeeze theorem)

Q: Find the best linear approximation to f on  the interval [-1,1].                        f(x) = x2

A:

Q: Use the intermediate value theorem to show that f(x) = e-x2− x has at least one root in the interval…

A:

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 16/x on the interval [0,…

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Q: Use the linearization of f(x) 1 at x = 4 to approximate f(4.3) . - f(x) =

A:

Q: Find the x-coordinate of the absolute maximum of the function f (x) = x³ – x² – x +1 on the interval…

A: Given

Q: Find all points c satisfying the conditions of the MVT for the function f(x)=x3−x in the interval…

A:

Q: Use the intermediate value theorem to show that f(x) = (e^−x^2)−x has at least one root in the…

A:

Q: Find the critical numbers of the function. f(x) = x8In(x) %3D X =

A: Consider the function  f(x)=x−8lnx

Q: Use the intermediate value theorem to show that f(x) = e −x 2 − x has at least one root in the…

A:

Q: Find the interval(s) on which f(x) = 2x^3-3x^2-12x+1 is concave up.

A: Given : fx = 2x3 - 3x2 - 12x + 1

Q: Find the linearization L(x) of f(x) at x = a. f(x) = a = 0 4x +3

A: topic - linearization of a function

Q: The domain of the finction f(x, y) = In(-x² - +1) is:

A: The domain of a function is the range of the values that can be input into the function. The…

Q: Find the absolute maximum value on (0, oo) for f(x)37-4x--

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: given that  y=xx2+1

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.