Q 6. If the function f(x) = 2x - 9ax + 12a*x+1 has a local maximum at x x1 and a local minimum at x= x, such that x, x, then a is equal to (a) 0 (b) 1/4 (c) 2 (d) either (a) or (b)

Q: 6. Find the absolute minimum and maximum of the function f(x) = x° – 12x+5 interval [0, 3]. on the

A: The function is given by fx = x3-12x+5 To evaluate : The absolute maximum and the absolute minimum…

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: 11.  Let h(x) = x^4 − 2x^2 + 3.(a) Find all critical points and use the First Derivative Test to…

A: Given information:The given function is shown below:

Q: (b) Find the global maximum and minimum values and indicate where they occur. f (x) ,x, ) = 2x, + x,…

A: Find the global maximum and minimum values and indicate where they…

Q: Find the points at which y=f(x)=4x−ln(2x)y=f(x)=4x−ln⁡(2x) has a global maximum, a global minimum,…

A: Given function

Q: Find the absolute maximum and minimum values of ƒ(x) = ex - 2x on [0, 1] .

A: Consider the given function.

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

A: f(x) = ax3 + bx2 + cx + d f(x) = 3ax2 + 2bx + c Now, f(x) = 0  at x = -2, 1 Hence , roots of above…

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 2 at x = −2 and a…

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Q: Find the absolute minimum and absolute maximum of f(x)=ln(x2+10x+16) over the interval [0,4]

A: It is given that, f(x)=ln(x2+10x+16)   over the interval 0,4we have to find absolute minimum and…

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: 1. Suppose that f(x) = -ar/2 + bæ/2. Reparameterize this function in terms of the location of the…

A: given fx=-ax32+bx12 differentiate the function with respect to x f'x=-32ax32-1+12bx12-1…

Q: 2. (a) Find the critical point(s) of the function f(x) = x2/3 on the interval -1,8| 2. (b) Use your…

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Q: 1. Find the absolute minimum and absolute maximum of the function f(x) = 2x-3x? on the closed…

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Q: f(x) = 3 x4-4 x3 -12 x2+1, has local minimum at x = OA. OB 2- OC. OD.

A:

Q: Соpy of The global minimum of f(x) = x³ – 4x over the interval -2< x<3 occurs at what value of x? O…

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Q: 1- If the critical point of the function f (x, y) = xy - x? - y? - 2x- 2y +4 is (-2,-2), this point…

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Q: 4. If f has a local minimum at x = 0 and a local maximum at x – 2, what can you say about f'(0) and…

A: f has a local minimum at x=0 and a local maximum at x=2.

Q: find the value of a so that the function f(x)=xeax has a critical point at x=6

A:

Q: Q#1 a. Find the critical point of f(x,y) = xy + 2x – Inx²y in the open first quadrant and show that…

A: Given f(x,y)=xy+2x-lnx2y f(x,y)=xy+2x-2lnx-lny fx=y+2-2x, fy=x-1y

Q: Identify the critical points of the function f(x, y) = x³ – 12x +y² – 3xy + 30 and the local minimum…

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Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: Let a > 0 and f(x) = x + . Then ƒ has An absolute maximum at x = -Vā A local minimum at x = Vā A…

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Q: f(x)D has a absolute minimum on [1,3] of 1/319 1/x

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Q: Suppose (2,1) is a critical point of a function f (x,y)· If D=4x – 5y and f=x+y, XX classify the…

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Q: Suppose f:(x)=x++x³- 6r2. Determine the value of x where f has a relative minimum value. O x=2 O x=0…

A: Function f'(x)=x4+x3-6x2 To find x where f has a relative minimum value

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a. a local maximum at x = -1 and a local…

A: Find first derivative.

Q: 5. The function f (x) = 2kx³ + 3x² + px – 3 has a local minimum at x = -1 and a point of inflection…

A:

Q: 1. Consider function f(x,y) for which = 24x² + 114y and %= 114x + 24y2. Wbich of the points (5, 5)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the points at which y=f(x)=4x−ln(2x) has a global maximum, a global minimum, and a local,…

A:

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

A: The given function is fx=sinx Differentiating w.r.t. x to both sides- f'x=cosx To find the critical…

Q: 1. Let r be a rational number with r > 1 and set f (x) = (1+x)" – (1+rx), for x > -1. Show that 0 is…

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Q: 2 3 The absolute minimum of f(x)= 3 x³ - 2x 0n [-1,8] is y =

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Q: 1 5. Define f(x, y) = x³ + y? – 2xy – 3x. (a) Find all the critical points of f. (b) Determine…

A: The solution is given below:

Q: 2. Find the global maximum and global minimum of f(x) = xe- on [0, 6].

A:

Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −4 and a…

A:

Q: 4. Find the minimum value of f(x, y) = xy subject to x² + y² = 8. 5. Find the minimum value of f(x,…

A: As per bartleby policy, I've answered only one question. Please upload it under another question.

Q: Can you help me step by step?

A: Since, the function f is an even function, so by definition of even function:

Q: what is the absolute maximum/minimum of: f(x)=xln(x/4) on [0.2,4]

A: Given, function is

Q: (b) Find the global maximum and minimum values and indicate where they occur. f(x1,x2) = 2x, + x, –…

A: Given,

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: 7- (a) If a is a constant and cannot be equal to 0, find the critical points of f(x) = 3a + 6x (b)…

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

A:

Q: 2. Consider a function f : R → R where S(x) = x³ – 3x for all æ e R. Identify all critical points…

A: Given the function fx=x3-3x  ,x∈R. To find the critical points and the local maximum and local…

Q: 5. Find the absolute maximum and absolute minimum values of f(x, y) = 3xy-3x– 6y+1 on the closed…

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

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Q: = 1 Find the minimum value of f(x, y, z) = 3x − y − 3z subject to x² + 2z² - - and x + y -z = 0.

A: