ain the rule of maximum and minimum using Derivatives with an example?

Q: 10. Using back calculation, find out what the function f(x) should be so that the second derivative…

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Q: When solving a first derivative test, a student calculates the following information. Help them list…

A: x=-3 and x=8 are critical points mean on these points there are local extremas. Given that:…

Q: a. Find the direction in which the function increase and decrease most rapidly at point Po. Then…

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Q: Explain how the real-world meaning of a derivative is related to the independent (input) and…

A: An independent variable a variable that stands alone and it doesn't change by the other variables we…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Given that the statement,   If a function has derivatives from both the right and left at a points…

Q: orthogonal trajectories are curves in which their tangents at all points of intersection are at…

A: An Orthogonal Trajectory, of a family is defined as the group of curves that intersects each curve…

Q: calculus Find the equation of the tangent line to the graph of f(x) = 4 - x2 at point (1,3).

A: given   f(x) = 4 - x2  point ( 1 , 3 )

Q: A thin observatory probe having the shape of a plate is probing a volcano in an xy −plane at a point…

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Q: (a) Find the linearization of f () = at a = 4. x+1 Enter the linearization using the equation…

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Q: Describe the First Principle method and the Power Rule method for finding the derivative. Which…

A: In first principle method the slope of the curve is used as a derivative This is called the first…

Q: rection where the directional derivative is minimum for the function f(x,y) = xy+x²- (2,1).

A: The given question is taken from the vector calculus in which we have to find the directional…

Q: Explain your understanding of the connection between the derivative of a constant and the slope of…

A: We need to establish a relationship between the derivative of a constant and the slope of the…

Q: relative maximum (x, y)

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Q: (b) Apply the First Derivative Test to identify all relative extrema. relative maxima (х, у) %3D…

A: Given query is to find relative extrimas

Q: Exercise (b) State the domain of the function. Step 1 Since the given function f(x) = x - is linear,…

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Q: f the first derivative changes from positive to negative at point c, what does this mean?     c is a…

A: Given that f is a function whose derivative changes sign from positive to negative at a point.

Q: ACTIVITY 1: Practice ! Apply differentiation rules in finding the derivative of the given functions.…

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Q: ntegration in calculus is generally used for:   computing the rate of change of one variable with…

A: Integration in calculus is generally used for

Q: How do derivatives arise in the study of motion? What can you learn about an object’s motion along a…

A: To determine the use of derivatives in study of the motion.

Q: Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable.…

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Q: Using calculus methods to find the length of the sides of the squares cut out so that the volume of…

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Q: Find the equation of a tangent line to the curve y= 2x3 - 3x² - 10x + 1 which is perpendicular to…

A: topic - equation of tangent line which is perpendicular to given line

Q: before a potential traffic accident one car is traveling at 128 km/h when the driver fully applies…

A: Given, the initial velocity of the car = u = 128 km/h  at initial time t = 0 Acceleration of the car…

Q: ensider a circle with center at the origin and with radius 3. a. What is the equation of the circle…

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Q: Using second derivative test for the critical points of the curve y = x³ - 3x2 9x + 20 , which of…

A: Let's find.

Q: -, 0) ; absolute minimum point at the point (-3, rema. e point (-4, 0) ; absolute and relative…

A: We have to choose the correct answer from the given options according to the given information

Q: Akash displacement from whom is is measured in MI by the function it is equals to

A: Akash displacement from whom is is measured in MI by the function it is equals to

Q: Richa< decline under question out of Scope> Find the equation of the tangent line to…

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Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

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Q: 4- x Find the equation of the tangent line tof-l at the point P (G, 1) for f(x) = x+1 Provide your…

A: Topic:- application of derivatives

Q: A manufacturer designs cylindrical cans with capacity (volume) of 1000 cubic centimeters (1 liter).…

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Q: true or false?  A negative derivative indicates that the curve is frowning.

A: TRUE Consider the graph for function x^3-x

Q: Determine the relative extrema for the function: y = 2xe* relative maximum at -1 relative minimum at…

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Q: a. Find the direction in which the function increase and decrease most rapidly at point Po. Then…

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Q: A differentiable function has the value y(-3) = 2 and the derivative value y'(-3) = 1. Approximate…

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Q: What can be said about functions whose derivatives are constant? Give reasons for your answer.

A: Consider f(x) be the function whose derivative is constant as shown

Q: Question: At this point in the semester, you have a variety of applications of the derivative…

A: Optimization , related rates, linearization and Newton's method.

Q: Examine the function for relative extrema. (If an answer does not exist, enter DNE.) f(x, у) %3 2x2…

A: As per the company guidelines we are supposed to solve only first question or first 3 subparts in a…

Q: ential equation of the family of curves y B are arbitrary constants

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Q: Sketch the graph of the function ? = x3-6x2+12. Using the ff. First derivatives (critical…

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Q: Write short example of numerical differentiation. (Subject-Numerical Methods), (Handwritten Solution…

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Q: Explain the concept of marginal cost. How does it relate to cost? How is it found? How does the…

A: The marginal cost measures the change in the cost that arises from unit increase in quantity. The…

Q: When solving a first derivative test, a student calculates the following Help them list all relative…

A: x=-3 and x=8 are critical points means on these points there are local extremas. Given that:…

Q: Using the linearization of f(x) = Arcsecr approximate the value of Arcsec1.7

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Q: Exercise 3 A mayor announces that the town's expenses are increasing, but at a decreasing rate.…

A: Given,  A mayor announces that the town's expenses are increasing, but at a decreasing rate.

Q: Find the derivative

A: Part c,Given,           y=lne5θ1+e5θ

Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A: We have fx=xx2+25Differentiate w.r.t…

Q: Part I: Find the derivative. Show all workow all y = e$x²-x 3.

A: The given equation is: y=e5x2-x

Q: Find the relative extrema, if any, of the function. Use the Second Derivative Test if applicable.…

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