Use the graph of f' shown in the figure below to answer the following questions. y y=f'(x) -1 1 2 3 4 5 (a) Estimate the value of x at which f has a relative minimum. If there is no relative minimum, enter NA.

Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: A function has a tangential gradient of 2sin3x. If the curve cuts the x-axis at, determine the…

A: A function has a tangential gradient  of 2 sin 3x.If the curve cuts the  x-axis at π3.To determine…

Q: Determine whether the following statement is true or false, and explain why. The cosine function has…

A: It is given that The cosine function has an infinite number of critical points where an absolute…

Q: Find the critical points, use the second derivative test, and determine the relative maximum and…

A: Answer

Q: Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local…

A: Given:   f(x) = x2 To determine whether f(x) has a local maximum or local minimum at the critical…

Q: (b) Argue that the graph of is decreasing for x near zero and that as x increases from zero, (x)…

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Q: at x = The function has a relative minimum of at x = The function is increasing on the interval(s):

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

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Q: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: Find the critical points of the function f(x,y) = y² + x²y+ x² – 2y and use Second Derivative Test…

A: Finding fx, fxx, fy,fyy and fxy and use D(x,y) = fxx . fyy - fxy^2 , to find relative maxima or…

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: Given a right circular cone with an altitude of 5 cm and a base diameter of 8 cm. If the diameter is…

A: volume of cone =Πr2h/3

Q: Find the slope of the curve y=x2−3x−4 at the point ​P(2​,−6​) by finding the limiting value of the…

A: Giveny= x2-3x-4 = f(x)at point ( 2, -6)as f(x) =x2-3x-yand f(2+h) = (2+h)2-3(x+h) -4…

Q: Find the maximum or local minimum f(x)=sinx.[0,4]

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Q: Is this calculus statement true or false: "We can determine that h(x) =x^4 has a minimum at x= 0…

A: Given function is  Then x=0 is critical point of h as h'(0)=0, but also h''(0) =0  Therefore,…

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: Find the relative extrema of f(x) = 8+72x – 9x? using both first and second derivative tests. f (x)…

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Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

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Q: s of 0 would be a minimum value on the graph of y = sin 0 over the interval [-27,0)?

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Q: What is (V and find the relative minimum point as indicated by the black dot on the graph at the…

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Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?

A: use average rate of change formula .

Q: 4. Given is the equation y = a) the critical points, b) classify the maximum and minimum point using…

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Q: 4y4 at the Find the maximum rate of change of the function f(x, y) point (5,1)

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Q: Find both first partial derivative Z = 15x x/y az az ду

A: As we know that: The the Power law: ddxxn=nxn-1 From the given problem: z=15xy

Q: Determine the gradient of the straight line which is tangent to the graph of f(x)= tan^-1(ln x) at…

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Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: The temperature in degrees centigrade (°C) at each point (x, y) on a curve 2x + y = 3 is given by…

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Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

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Q: What

A: The correct option is (B).

Q: True or false: The minimum value of the function y = 2 sin x + 1 is -1._______

A: True or false: The minimum value of the function y=2 sin x+1 is -1.

Q: Q4/ Explain the rule of maximum and minimum using Derivatives with an еxample?

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Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

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Q: Find the global minimum of the function f (x) = 1+x² on the interval (-∞, 0) . Write DNE is there is…

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Q: Determine the indicated (in the attached image) partial derivative of  f(x, y) = 3x3y2 + ln(2x2 -…

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Q: Find the critical points of the function f(x, y) = y² + x?y+x² – 2y and use Second Derivative Test…

A: Follow the steps below to yield the result . Calculate . Find the critical point by solving the…

Q: Find the critical point of the function f(x, y) = 9x 3y- - In(\r+ y|). c = || Use the Second…

A: Let f(x,y) be any function of two independent variables x and y supposed to be continuous for all…

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find the indicated partial derivative.

A: Given that, f(x, y) = y sin-1 (x, y) We have to find fy(1, 1/2).

Q: ) Use the second derivative test to classify each critical point of f (x,y)=-x' +4xy- 2y² +1 as a…

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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: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does…

A: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does…

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…

Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

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Q: Let f(x,y) = x^2 y + e^xy sin y.   At Point (1,0) State the direction where the function…

A: Given: fx,y=x2y+exysiny