f (x) = x 2 satisfies the Horizontal Line Test on the domain {x : x > O}.

Q: 4) Let f(x) = x* – 2x -1 be defined on the interval [-1,3]. Find the maximums and the minimums.

A: The given function is defined  f(x) = x4 - 2x2 - 1 Over [-1,3] To find minimum and maximum value 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 local maximum and local minimum values of f using both the first and Second derivative…

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Q: Find the critical point for f and then use the second derivative test to decide whether the critical…

A:

Q: The function f(x,y) =26-2x²-y² is continuous at point (2, -3). .A True .B False

A: The objective is to determine whether the statement, " The function fx,y=26-2x2-y2 is continuous at…

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. x2…

A:

Q: 1. f(x) = x² +x – 1 for all values of x -

A:

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

A:

Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

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: Let f(x) = x³ + 3x2 + x + 3. Determine the points f where the tangent line is horizontal on

A: to find the points where the tangent line is horizontal we have to first derivate the function and…

Q: Find the absolute maximum and minimum of f(x)=x² - 3x on the interval [-1, 3]. Express your answer…

A: The points of local maximum and minimum can be obtained by differentiating the function and equating…

Q: Find the absolute maximum and minimum values of f(x)= x2/3,on the interval (2,3).

A:

Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval [0, 4]

A: Use critical value and end points for absolute maxima and absolute minima.

Q: Find the values of k that make the function continuous. Jk² + 18x, x > -3 f (x) = kx, x < -3

A:

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: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Find the critical point of the function f(x, y) = 1 - x – 6x² – 8y + 3y?

A:

Q: Find the absolute maximum and minimum of the function  f(x)=xe-x on  the interval [-1,1]

A:

Q: Find the critical point of the function f(x, y) = 8 – 4x + 7x² – 6y – y? - -

A:

Q: Find the absolute maximum and absolute minimum f(x) = + x2 24x over the interval 2, 6|. -

A:

Q: Find all the critical numbers for the function g(x) = % xª -- x3 - 5x?

A:

Q: Consider the function f(x) = z over the interval (-2, 2). Does the extreme value theorem guarantee…

A:

Q: Find the absolute maximum value of f(r)= x-2x+ 16 over the interval 0, 5

A:

Q: 3. What is the maximum value of the function f(x) = 2x- 2x + 6 in the interval %3D [0, 2]?

A: Introduction :

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

A:

Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

A:

Q: (a) find the local linearization of f(x)=fourth root(x) at x=16 (b) Use the linearization to…

A: It is a linear approximation problem

Q: Find the extrema of f(x) = 3x4 − 4x3 on the interval [−1, 2].

A: The given function f(x) = 3x4 − 4x3 on the interval [−1, 2].

Q: Find the local maximum value of f using both the First and Second Derivative Tests. f(x) = x + V1 -…

A: First calculate critical point at which either local maxima or local minima will occur by putting…

Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

A:

Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

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

A: Given function is f(x) = x3 - 3x2 ; -2 ≤ x ≤ 4 We have to find its minimum value.

Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval (0, 4]|

A: The absolute vale in the interval [0,4] for f(x) will be either at critical points or at end points.

Q: Find the absolute maximum of f(x) = x³ – 12x + 1 on the interval [0, 4]. -

A:

Q: Find the absolute maximum and minimum of f(x)=3x^3-x+1 on the interval [0,1]

A:

Q: Determine a minimum of f(x) = x² + 3x², Starting from x, = (6,3) = 6i + 3j and applying the method…

A: The given function is fx=x12+3x22 . The initial point is x0=6, 3. Let it be X0=6, 3. The gradient of…

Q: Find the absolute extrema of f(x) = 2x3+3x2−12x on the interval [0, 2]

A:

Q: 1. Can Rolle's Theorem be applied to y = (x – 2)3 on the interval [0, 4]? Justify.

A: Check differentiability at x=2

Q: Find the absolute maximum value of f(x) = x² – 2x + 12 over the interval [0, 5]

A:

Q: f f is a differentiable function with derivaitve f' x^2+2x-3, then f has a realtive minimum

A: We are given the derivative of the function f which is f'(x)=x2+2x-3, and we need to find relative…

Q: Find the absolute maximum value of f(x) = x2 – 2x + 18 over the interval [0, 5]

A:

Q: Use the second derivative test to locate all local extrema for the function f(x)=x3−32x2−18x. At…

A:

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

A:

Q: The value of Wronskian of two functions y, =7* and y2 =7** is

A:

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

A: Given that : The function f is  fx=13x3-4x   ,..........(1) To find: The value of x∈-5, 5 for which…

Q: Find the absolute maximum value of f(x)=(x)(x-1)(x+1) on the interval [-1,1].

A: Definition used -   Absolute maximum value of function - First we equate the first derivative of…

Q: Find the absolute maximum and absolute minimum of f(x) =2x – 3x² – 36x + 2 on the interval [0,5]

A: Before finding absolute maximum and absolute minimum of any function over the given interval we need…