Consider the graph of the function f(x) = 2 x^(5/3) - 5 x^(4/3), the relative minimum is located at a point O (0,0) O (1, -3) O (2, -16) O (8, -16)

Q: 2. As an application of partial derivative of multi-variable functions, provide one page abou…

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Q: An open–top box with a square base is to be constructed from two materials, one for the bottom and…

A: Given The volume of the box must be 18 cubic feet

Q: What are the conditions for a critical point of a function ƒ?

A: If "c" is to be a critical point of a function f , it has to be a solution of f'(x)=0 To be an…

Q: Find the minimum and maximum values of the function y = 8Vx² + 1 – 7x on the interval [0, 8] by…

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Q: Sketch the graph of a continuous function on (0, 4) with aminimum value but no maximum value.

A: Given: The interval of a continuous function is (0,4)

Q: Find the minimum and maximum of the function y = z - 12005z on [-8, 8] by comparing values at the…

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Q: Where does a local minimum occur?

A: given,      Local minimum .

Q: Find the absolute extrema of the function on the closed interval. 4x Rx) =2+25 [-6, 6] %3D minimum…

A: f(x)=4xx2+25

Q: Find the critical points of the function and examine these points (local maximum, local minimum or…

A: Here, it is given that f(x,y)=-x3+2y3+27x-24y+3

Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: Classify the critical point (0,0) for for all - 0 <µ<0. 2 -

A: given system of matrix x'y'=022-μxy     for all -∞&lt;μ&lt;∞ claim- to classify the critical point…

Q: Compute the required derivative approximations for the functions at the specified location, for the…

A: The given problem is to find the first derivative of the given function y=x3+4x-15 at x=0 using two…

Q: at the point (2, –1). Find the maximum rate of change of f(x,y): x2 + Y

A: For maximum rate of change we need to calculate magnitude of gradient bat point (2,-1)

Q: Find the absolute extrema of the function on the closed interval. y = = 3x2/3 - 2x, [-1, 1] (x, y) =…

A: Solution:-

Q: What are the maximum and minimum values in application of derivatives?

A: We have to define the maximum and minimum values in application of derivatives.

Q: Find the absolute extrema of the function on the closed interval. (x) = 7x2 + 1, (-1, 2] minimum (х,…

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Q: Sketch the graph of a function on [-1, 2] that has anabsolute maximum but no absolute minimum.

A: According to the given information, it is required to sketch the graph of the function on [-1,2]…

Q: 2. Let f: (0,-1→ R be a function defined by f (x) = x¯* for every x E (0,-1. Sketch its function…

A: This is a problem of the application of differential calculus.

Q: A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide…

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Q: Find the absolute maximum and absolute minimum values off on the given interval. Ax) = (x²-1)°,…

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Q: Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine…

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Q: Sketch the graph of a differentiable function y = ƒ(x) that has local maxima at (1, 1) and (3, 3);

A: given that a differentiable function y=f(x) and has s local maxima at (1,1) and (3,3) local maxima…

Q: If the function tends to infinity at the endpoints of the interval, then the function must take on a…

A: A continuous function defined on open interval with range equal to a closed interval. Consider a…

Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

Q: Find the exact location of all the relative and absolute extrema of the function. f(x) : = x In(x)…

A: Given function, fx=xln(x)

Q: Explain the rule of maximum and minimum using Derivatives with an example?

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Q: Find a cubic function whose graph has a relative minimum at (0, 1) and a relative maximum at (3, 5).…

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Q: 1) Explain the differences between an absolute minimum and a local minimum.

A: An absolute minimum occurs at the x value where the function is the smallest, while a local minimum…

Q: 2. Use an example to show how to use the First Derivative Test for critical points

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Q: Find the absolute extrema of the function on the closed interval. f(x) = x³ - (-1, 4] minimum (x, y)…

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Q: find any locl maximum and locl minimum values by using first derivative: f(x)-x-2x

A: Given :           f(x) = x4 - 2x2

Q: The critical points of a function f(x) occur at x = 2 & x = 6 and its 8 second order derivative is…

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Q: As an application of partial derivative of multi-variable functions, provide one page about Lagrange…

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Q: On the interval 2 < x < 4, there is a relative… •maximum •minimum •increasing •decreasing •constant

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Q: Explain how to determine Partial derivatives for x-value ?

A: Partial derivatives :- Let z=fx,y be function of two independent variables x and y. If we keep y  as…

Q: Find the relative extrema of f(x) = 3 + 70x – 7x² using both first and second derivative tests. f…

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Q: Explain how to find a first partial derivative of a function oftwo variables.

A: To get the first partial derivative of a function z = f(x, y) with respect to x we have to…

Q: b- find any locl maximum and locl minimum values by using first derivative: I(x)=x-2x

A: Given, f(x)=x4-2x2

Q: The origin is a critical point for the function f(x, y) = 15 − x^2y^2 and ∆(x, y) = 0 there, i.e.,…

A: As x2y2 is always positive (i.e., for all values of x and y),       15 - x2y2 &lt;= 15 (maximum)…

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = 1+8x - 3x2

A: i) The given function is fx=1+8x-3x2. Note that, the above polynomial function is real and defined…

Q: local

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Q: To find the absolute max and min values of a function g (x) on the interval la, b): extreme values…

A: To find absolute maxima and minima

Q: Use the second derivative test to identify any critical points and determine whether each critical…

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Q: 311. When you find the maximum for an optimization problem, why do you need to check the sign of the…

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Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Find all critical numbers and use the Second Derivative Test to determine all local extrema.

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Q: Let y=X^x, X&gt;0. Find the x where the function has a minimum value What is this minimum value?

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Q: Suppose you find the linear approximation to a differentiablefunction at a local maximum of that…

A: It is known that the linear approximation of a differentiablefunction at a local maximum of that…

Q: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2