Find the absolute maximum and minimum values of f(x) = (z² + æ)f over the interval [-3, 4]. and it occurs at x = and it occurs at x = absolute maximum is absolute minimum is

Q: 2/3 Q31 3x-2x, [-1,1] =3(x)-2 2- -1/3 -1/3 2x 2(x"?-1)=0 -1/3

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Q: Find the critical points of the function f(x) = x³ + 1¹5 x² + 50x + 8. Use the First Derivative Test…

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Q: Find the critical points and the intervals on which the function f(x) = x* – 9x2, (x > 0) is…

A: Given: The function is  fx=x4-9x32, x> 0   To determine: The critical points and the intervals on…

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: Find the absolute maximum and minimum values of f(x) = 2x³ + 3z² + 7z – 5, if any, over the interval…

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Q: Find the points of local minimum and  local  maximum of the functions f(x) = sin2x where x belongs…

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Q: 2. Find the local maximum and minimum values and saddle points (if any) of the function f(x, y) = xy…

A: Here, the given function is: f(x,y)=xy-2x-2y-x2-y2

Q: Find the absulote maximum of x40-x20 on the interval [0,1],also find its absolute maximum value

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Q: a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and…

A: fx=xlnx Differentiating with respect to x, we get f/x=dxdxlnx+dlnxdxx    Because,…

Q: Find absolute maximum and minimum points, if they exist, of f(x)=x^3+x^2-X+1 on the interval…

A: We need to check value of f(x) on critical points and boundary values of interval to find absolute…

Q: (b) Let f(x) = 12x35+ 15x* – 40x³ + 17. Find the critical numbers, and show what the Second…

A: f(x) = (12x 5+15x4 -40x3 +17.   critical points   f'(x) = 0   60 x4 + 60x³-120x²  = 0.   x² ( 60…

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: For the function f(x)= 6x-20arctan (x/3) find the absolute maximum and the abusolute minimum on the…

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Q: Determine the values of constants a, b, c, and d so that ƒ(x) = ax3 + bx2 + cx + d has a local…

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Q: 7) a) Find all the critical points of the function y = h(x) = ln(x +1)° – 2x + 5. b) For each…

A: Given      y = ln(x+1)^6-2x+5

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

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

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Find the absolute maximum/minimum of function f(x) = 4x3 - x2 - 2x %3D for interval of [0, 1]

A: The absolute maximum of a function in interval a,b is the maximum function value over this interval.…

Q: Find the critical points of the function f (x, y) = - x2+ 4xy+ xy2 and determine whether the…

A: We have  fx,y=-x2+4xy+xy2 Differentiating partially w.r.t. x and y, we get…

Q: Let f(x) = e^(2−x^2). Find the x-coordinates of all critical points of the f. Determine whether each…

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Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: f(x,y)=x2+4xy we have to find the critical points.

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: (7) Does the extreme value theorem tell us that f (x) = ! has an absolute maximum and absolt minimum…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: Differentiate the given function with respect to x and equate it to zero,…

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x²

A: Points of local extremum can be calculated by using the first derivative. These are points which…

Q: 15. For this function find the coordinates of points on the graph that are local maximums or…

A: Local maxima and minima

Q: The profit function (in millions) for a beverage company for the years 2008 through 2015 can be…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: What is f(x) = x +1/x absolute maximum and absolute minimum at the range [0.2, 4]

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Q: Find the absolute maximum for the function over the specified domain. y = a² +1 over [ – 1, 4]…

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Q: Find the relative extrema of f(x) = 3 +90x – 9x² using both first %3D - and second derivative tests.…

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Q: find all critical points of f(x) = x²e², and use the second derivative test to determine if each…

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Q: Find the absolute maximum and minimum values of f(x) = -(x² + x) interval [-3, 4]. over the absolute…

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Q: Find the absolute maximum and minimum vaules of the funct ion g(x)= (x^2-3x+4)/(x-1) on the interval…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: We will use first and second derivative test for minima and maxima.

Q: f f is a differentiable function with derivaitve f' x^2+2x-3, then f has a realtive minimum

A: We are given the derivative of the function f which is f'(x)=x2+2x-3, and we need to find relative…

Q: Consider a differentiable function f with domain R and derivatives f'(x)=-aebx(1+bx) and…

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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: (1) Find the derivative of the function f(x) = 2x³ - 12x² +4 and use it to find the critical numbers…

A: Solution is given below:

Q: Let f(x)=kx^-1+x^2 For what values of k, function f(x) has a relative minimum but not a relative…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Find the minimum and maximum values of f(x) = on the interval [6, 7] by comparing values at the…

A: Consider the given:…

Q: f(x)=12+4x-X ', [o,s]

A: We will use derivative test to find the maxima and minima.

Q: Where are there local minimum(s)/maximum(s) f(x)=3(2x-1) -4(x+1)?

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Q: The profit function (in millions) for a beverage company for the years 2008 through 2016 can be…

A: Given profit function is f(x)=-26x2+728x-2643where x=8 is year 2008.

Q: 3 The absolute minimum value of f(x)=x³ on the closed interval [-1,8] is a) 0 b) -1 c) 1 2 d) -…

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Q: Find the absolute maximum of h(x)=x2 −x−2 over [−3,6]. Enter only the y-coordinate of the maximum.

A: Determine the  derivative of the function  and find the critical points.