Q2:A/ Consider the function f(x) =; a-what are the first and second derivatives? b-what are the critical points for the functions? c-what is f" evaluated at these critical points? 11x+3

Q: Q2/ A/ Show that the functions f(x) = sin-1() and g(x) = 2tan-Vx, have the same derivative. %3D

A: Given : f(x)= sin-1 ( x-1 / x+1 ) g(x) = 2 tan-1 (√x)

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

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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: 3. Suppose the function f has second derivative f"(x) = x2(x – 3)(x+2)*(? – 1). = T- (a) How many…

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Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

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: Use the first derivative test to find the location of all local extrema in the interval for the…

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Q: Find the approximate error, relative approximate error, and absolute relative approximate error of…

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Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. 1 f(x) =…

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Q: Suppose the function f(x) has the derivative f'6): 4x-122 -8 こい x-) G。 C) what are the x-values of…

A: Here given derivative of function f(x) as f'x=4x-2x+12 (a) To find the critical point of function…

Q: Given the function f(x) = (x-4)2 + (y-5)2 (i) Find the critical points.  (ii) Using the second…

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Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

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Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

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: 2. Let f(x) = /1 – x² . Find f(8) (0), i.e., the eighth derivative of ƒ evaluated at the point 0.

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

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: Find the critical points of the function. Then use the second derivative test to classify the nature…

A: Introduction: If the critical point of the function fx,y is a,b. then fx,y has local minima at a,b…

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Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

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Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: Q2:A/ Consider the function f(x) = 11x+3 -what are the first and second derivatives? -what are the…

A: We will answer the first three subparts of the first question as per our guideline. Please resubmit…

Q: given the function f(x) = (x+4)^2 + (y-2)^2 (i)find the critical points (ii)using the second…

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Q: Solve for the derivative of t y =2 V3-z Previous

A: This is a basic differentiation problem

Q: Q:1 Find the second derivative of f(x) = 2x5 - 3VX7 at x = 1 rounded to five decimal places.

A: To find the second derivative of  f(x)=2x⁵-3x7/3 at x=1

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

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Q: 4. Find and classify the critical points of the given function by using Second Derivatives Test. 1 1…

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Q: Consider f (x) = x* – 8x2 + 1. a. Find the critical values. b. Use the first derivative test to…

A: We have , f(x) = x4 - 8x2 + 1.  To find : Critical Values.

Q: What role does the denominator of f'(x) play in finding the critical points (in other words, what do…

A: The given data is: f'x

Q: Find the relative extrema of f(x) = 9 + 30x – 5x? using both first and second derivative tests. f(x)…

A: Derivative one time and equate it to zero to find the critical point. Derivative second to find the…

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

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Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

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

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Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

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Q: Find the first and second derivatives of the function. f(x) = x/(7+x2) Identify the intervals on…

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Q: Find the relative extrema of f(x) = 2+ 90r 5x using both first and second derivative tests. f(x) has…

A: We can find the relative extremum as below

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: 15. Find the linearization of f(x) = vx +1 at a = 15 and use it to find an approxima- cion to v15…

A: Given: f(x)=x+1 at a=15

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

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Q: Find the relative extrema of f(x) = 4+ 40x – 5x? using both first and second derivative tests. f (x)…

A: Explained below

Q: (1) For what value c on the interval [-10, 10] can the second derivative test be used?

A: Second derivative test is used to check if a critical point is a local minimum or maximum.  So we…

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: 5)Let f ( x ) =3x4 + 4x3 Find the derivative. b)Find the critical numbers.

A: Given problem:- 5)Let f ( x ) =3x4 + 4x3   a) Find the derivative.   b) Find the critical numbers.

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: Given function, fx=e-x a=-0.1 Formula for the linearization at x=a is given by Lx=fa+f'ax-a

Q: * The tangent line to y = f(x) at (-4, 10) passes through the point (-5,-10). Compute the following.…

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x) =…

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