The function f(x) is defined below. What is the end behavior of f(x)? f(a) = -10a° + 400 - 2400 1200x? - 3520x +250x as x -o, y -0 and as x 00, y 0 as x -00, y o and as x 0o, y -0 as x -o, y -o and as x 00, y -O as x -0, y o and as x , y ∞ Submit Answer

Q: Find the local extreme values of the function: f(x,y)=xy-x^2-y^2-3x-3y+12.

A: It is given that, fx,y=xy-x2-y2-3x-3y+12We have to find the local extreme values.

Q: B- Find the local extreme points of the function f(x, y) = 4xy - x - y^.

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Q: This function has: 1) A y intercept at the point 2) x intercepts at the point(s)

A: Given,  fx=2x2+11x+123x2+10x+3 The x-intercept, y-intercept, and vertical asymptotes are to be…

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: nd the points where the function f(x) = (x² – 1)³ is decreasing, -

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Q: The graph of the linear function f(x) passes through the point (x, y) = (1, m), where m is the slope…

A: Given:Graph of f(x) passes through the point (x, y) = (1, m), where m is the slope of the line.

Q: Find the local extreme values of the function ƒ(x, y) = xy - x2 - y2 - 2x - 2y + 4.

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Q: Find d2y/dx2 as a function of t if x = t - t2 and y = t - t3

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Q: Find the formula for a function of the form y=be^((-(x-a)^2)/2) with its maximum at the point (0,5).…

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Q: (b) Determine the domains and range of this function: y = v1 -x-

A: The given function is y=1-x2 the domain of the function is -1≤x≤1 In the interval notation the…

Q: f(x) = 4x^3-(x+9)^1/2 What is the interval or intervals on which the function is differentiable on…

A: Refer  to the question the provided function is f(x) = 4x^3-(x+9)^1/2.

Q: Find the point on the graph of the function that is closest to the given point. Function Point f(x)…

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Q: The function f has a continuous second derivative, and it satisfies f(-8) = 5,f'(-8) = 0 and f"(-8)…

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Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Given equation is: y = -3x - 16

Q: The function f(x, y) = -3y + 2√√ry is a

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Q: B. Find and classify the extreme points of function f(x, y) x* +y-4xy-1.

A: Maxima minima of two variables function

Q: Find the the stationary points and the local extreme values of the function f(x, y) = −2x/x2 + y2+1

A: The objective is to find the stationary points and the local extreme values for the function…

Q: Q2:- Find the maximum value of the function f(x,y) 49-x-y? on the line x+ 3y = 10. %3D

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Q: Find a function of the form y = Asin(kx) + C or y= Acos(kr) + C whose graph matches this one: is…

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Q: Find f'(2) if y = f(x) is the nonnegative function defined for x, y > 0 by the equation x" = y?.

A: To find f’ (2), if y = f (x).

Q: 1. What does it mean to say that the equation +y 6ry defines y as an implicit function of r? %3|

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Q: (B) Use the second derivative test to find the maxima and minima for f(2) = 22 - 15x + 1. 3 %3D

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Q: The function f(x)=x2 is decreasing on the interval...................... .

A: Given,f(x)=x2 f(x)=x2 On differentiating both sides w.r.t x we get: f'(x)=ddx(x2)⇒f'(x)=2x Now, we…

Q: Consider the implicit relation yx +1= 7y. In the box below, solve the equation for y as a function…

A: In this question, we have to separate y in terms of x.  i.e. y=f(x)

Q: Find the linear approximation of the function below at r = -1 and use it to approximate f(-0.8). -7x…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: V4 – x2 – y? In(y – x) - Find and sketch the domain of f(x, y) -

A: Given,fx,y=4-x2-y2lny-xRoots are:y=-4-x2y=4-x2Domain is: (x,y)∈R2:log(y-x) ≠0 and x<y and x2+y2≤4

Q: The path of a diver is modeled by 24 *+ 13 f(x) = - where f(x) is the height (in feet) and x is the…

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Q: 1. Find the intercepts of the function. f(x)-x* +2 а.

A: Given data÷

Q: Vx-1 for the function f(x) = -! by using quotient rule. Vx +1

A: Use quotient rule for derivative

Q: Fxy(x, y) is a monotonic and non-decreasing function of both x and y.

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Q: Find the absolute maximum of the function f(x) = x-x-x On the interval - 10 sxS2 (a) 14 (b) 13 (e)…

A: To find absolute maximum and minimu , first, we need to find critical points. These are the points…

Q: e4z f (2) = 27 + 38 at how many points the function f (z) is discontinuous ?

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Q: Example:Find a²y as a function of t if x = t – t2,y =t-t3. dx²

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Q: State the interval of the function g(x) = E-x is %3D

A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: Use the First Derivative Test to find the x-value(s) at which the function f(a) = + 4x? 2 9x? + 4…

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Q: Q3. At what points are the functions continuous y =-3x x+3 y = x2-3x-10' y = (2x - 1) X-2

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

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

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Q: The function f(x) = x3+Ax+B has a stationary point at (-2,3). Find the values of A and B .

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Q: (A) Find the absolute maxima and minima for x3 y = - x + 5 over 3 [-V2, v2]. (B) Use the second…

A: When on critical point f''<0 then that critical point give local maximum value of f(x)  When on…

Q: Consider the function f(x) = i + x². How does this function essentially behave for large positive…

A: The Given Function f(x) contains rational function x/(x2+1) and polynomial function function…

Q: Find and classify the extreme point of the function f(x, y) 3y2x + x³ - 3y3 - 3x? + 2.

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Q: f(x) = 4x^2-12x+7   how is this function concave wherever it is defined?

A: Given:

Q: 1. What linear function,  y has f(0) = 8 and  f(7) = 14?

A: Linear function

Q: B. Find and classify the extreme points of function f(x, y) = x + y - 4xy-1.

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Q: Find an equation for the linear function which has f (0.5) = 0.8 and f (0.8) = -0.3. f (x) =

A: We have to find the linear function where, f0.5=0.8 and f0.8=-0.3 We know linear function form,…

Q: Find the linear approximation of the function below at x = -1 and use it to approximate f(-0.8). -7x…

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Q: x², -2sx<1 (x+1, 1sx<2 For the piecewise-defined function f(x) = }

A: fx=x2,-2≤x&lt;1x+1,1≤x&lt;2

Q: The range of the function y= 16-x2 is the interval [0, 0)

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Q: For the function y = (f ¹)'(-4)= f(x) = x² + 4x - 3, x ≥ - 2, find df-1 dy y=-4

A: Introduction: For a function y=fx, its inverse function is represented as x=f-1y. It is not…

Q: The revenue function of a company as a function of units sold x is R(x)=2x−0.005x2. How many units…

A: Given revenue function:

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.