3) Let f(x) represent the path of a particle. x* 1 f(x) =+ x 2 1 16 2x2 Suppose the particle starts at (1, f(1)) and travels along the path to (a, f (a)). If it is known that the particle travels a distance of 3 units, what is the value of a?

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

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Q: For the function f (x) = 3x° – 5x* – 200x³ , find the critical value for f"(means find the x…

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Q: For the function y = -2+5 sin (x-2), what is the maximum value?

A: Given,Function y =-2+5sinπ12(x-2)

Q: Find a point c satisfying the MVT for the given function and interval. 2 y = x3 [0,8]

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Q: Determine the equation of the quartic function with the following characteristics x-intercepts at x…

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Q: The function f(x) = 2x – 42x + 270x – 2 has two critical nu The smaller one is x = and the larger…

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Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 3x2 – 4x + 8 has a tangent…

A:

Q: Find the values of a and b such that f(x) = x³ + ax² + bx + 5 has x = 1 and x = 2 as critical…

A: The function f(x)=x3+ax2+bx+5 has critical points at x=1 and x=2

Q: 7. Find the absolute maximum and absolute minimum values of f(z) = 2x – 3r2/3 on the interval…

A:

Q: 38 Find the critical numbers of the function. 25. f(x) = x³ + 3x² – 24x %3D -

A:

Q: If the total revenue function for a blender is R(x) = 40x − 0.01x2   where x is the number of units…

A:

Q: 1. Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) =…

A:

Q: The function f(x) = 2x3 – 39x? + 240x + 9 has derivative f'(x) = 6x? – 78x + 240. %3D f(x) has one…

A: Given data:   The expression for the given function is f(x)=2x3-39x2+240x+9. The expression for the…

Q: The average cost (in dollars) incurred by a media company each week in pressing x compact discs is…

A:

Q: Suppose the cost per hour incurred in operating a cruise ship is 5a + b^4v^3 dollars per hour, where…

A: Step:-1 Note:-  your cost expression is not clear here as it can be 5a+b4v3   or   5a+b4v3 , So i am…

Q: giver yn f(५) ५) -2x + 3, + 2, find of ax

A:

Q: The function f(x) = 2x – 45x + 300x – 5 has two critical numbers. The smaller one is x : %3D and the…

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Q: Please show steps.

A:

Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: Find the critical numbers of the function.…

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Q: Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx

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Q: 8. If f(x) = 4 sin x + 6 and g(x) = 3x + 5, what is the maximum value of f(g(x))?

A: Solution is given below

Q: If the total revenue function for a blender is R(x) = 84x − 0.01x2 where x is the number of units…

A:

Q: Find the maximum of f(x) = 30x4 − 121x3 + 60x2 + 64x USING Newton’s method (x0 = 4, εs = 1%)

A: Given, fx=30x4-121x3+60x2+64x With initial point, x0=4 Differentiating the given equation up to…

Q: Find a 4th degree function that has solutions X=-4-2/3 and x=-4+2/3, x=2i and x=-2

A: See the attachment

Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

Q: 3. Find the fixed point(s) of f: [1, ∞)→→ [2, ∞) defined by f(x) = √²+x.

A: 3) To find: fixed points of f:[1,∞)→[2,∞) defined as f(x)=x2+x.

Q: Find the number of units x that produces the minimum average cost per unit C in the given equation.…

A: given

Q: In this problem, we'll walk through the steps to find the area of the rectangle bounded by: The line…

A: Topic - equation of lines Note :As per bartleby guideline  if more then three subparts are asked…

Q: 1) Find the absolute extremum values of f(x) = x² – 3x + 12 over the interval [1,3]. [2 marks] %3D -

A: Given: fx=x2-3x+12 over the interval 1,3

Q: An animal feed company must produce 200 kg of mixture consisting of ingredients x and x2.x costs 3…

A: we will first formulate the LPP using the given statements and then we will find the optimal…

Q: It is given that at x = 1, the function x4 - 62x2 + ax + 9 attains its maximum value in the interval…

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Q: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

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Q: Use the linear approximation (1 + x)k = 1 + kx to find anapproximation for the function ƒ(x) for…

A: It is known by linear approximation that 1+xk=1+kx for the values of x near 0. The given function is…

Q: Show solution/process. 1. f(x) = 2x² – 4x + 5 at the point (–1,11) 2. f(x) = v25 – x² at the point…

A: Since there are more than one question, only one question can be answered. The function is given by,…

Q: Find all critical points for the function f(x)= x²e!-2¤. %3D

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Q: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?

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Q: 3. Find a linear approximation to the function at the point x = 3. y = f(x) = x²e + 8x

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Q: Find the critical numbers of the function of f(x) = (x^3)/3 −16x

A: Given function is : fx=x33-16x To find the critical number of point.

Q: On the graph of f(x)=cosx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: We know,  -1≤cos x≤1 for any real value of x.

Q: The function f(x) = 2x – 33x + 60x – 8 has two critical numbers. The smaller one is x = and the…

A: To find the critical point use the differentiation .

Q: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: (b) Show that f(x) = ln(x + 2) has a unique fixed point in [0, 2].

A:

Q: 2. Integrate the function (x+2/x)ax using multiple-application trapezoidal rule with n= 3

A: Trapezoidal Rule: ∫abf(x) dx≈∆x2(f(x0)+2f(x1)+ ... +2f(xn-1)+2f(xn))where ∆x=b-an

Q: The graph of f​(z​)=16^z passes through the points (−1,x ), (0,x)and (1,x) simplify

A: The equation of the graph is given that: f(z)=16z. So, when it passes through the points (-1,x), it…

Q: 1. f(x) = x2 + x – 1 for all values of x %3D

A: A detailed solution is given below

Q: Find the roots of the given equation where f(x) = 0 with the stopping criterion of 0.001. f(x) = (x…

A: The fixed-point iteration method uses the formula: xn+1=ϕ(xn) to perform the iteration and to…

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.