For g(t) = t2 / (t2 + 3) a. Find all critical numbers of g. b. Find the absolute maximum and minimum of ? on the interval [-1,1].

Q: Find constants a and b in the function f(x) = axe“ such that fE) = 1 and the function has a local…

A: The given function is fx=axebx. It is given that f15=1. So, f15=a·15·eb·151=aeb55aeb5=5

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Q: 4. In each of Exercises (a) to (d), find all critical numbers of the given function and use the…

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Q: Find the absolute maximum and absolute minimumvalues of  f on the given interval.

A: Given equation is Differentiating both sides, we get Now, we will wind critical points of f(t) in…

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Q: Find the critical numbers of the function.…

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Q: f (x, y) = 5ye" – e5x – yð

A: for critical points equate the first derivative wrt x and y to zero.

Q: For the function f(x, y) = (3x + 4x')(k'y² + 2y) where k is an unknown constant, if it is given that…

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the critical number(s), c, of the function: f(x) = 3Vx· e-5x

A: Given: fx=3x.e-5x

Q: For function f(x,y) to have minimum value at (a,b) value is? 1) rt - s>0 and r0 and r>0 3) rt - s?0…

A: For a function fx,y to have minimum value at a,b, which of the given condition is true? 1)…

Q: Find the critical numbers of the function.

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Q: Find the absolute maximum and absolute minimum values of f(x) = x ln ,e). on

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Q: 5. Determine the minimum value of f(x) = e* – 3x on the interval [-1,1] [T:3] %3D

A: Topic:- Maxima minima Minimum value of f(x) is 1.

Q: Let f(x) = x? (6 – x)3 (a) Find all critical point of f(x). (b) Classify each critical point as a…

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Q: Given a function f ( x, y) = x3 + y3 + 3x2 -18y2 + 81y + 5 The function has four critical points…

A: The given function is fx,y=x3+y3+3x2-18y2+81y+5. Obtain the critical points as follows:…

Q: 6. Find a cubic function f(r) = ar³ + bx² + cx +d that has a local maximum value of 3 at r =-2 and a…

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Q: Suppose that t hours after the injection of x milligrams of adrenalin the response is R units, and…

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Q: Find the critical numbers of the function: f (x) = e²–9z

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Q: find the critical point and classify the function f(x,y)= x3 +y3 - 6xy

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Q: 3. Find all the critical points of the function f(x, y) = e(x² + y²) and determine whether each of…

A: Given function is f(x, y) = ey(x2 + y2)

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

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Q: For the function f(x, y) = x4 + yA - 4xy on the set D = {I(x, y)| 0<x< 2, 0sys 3}, calculate the…

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Q: Find the critical points of the function f(x,y)= -2x^3 -4xy +2x -5y -1 and classify them as local…

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Q: 2. Find the absolute maximum and absolute minimum values of fon the given interval. f(t) = t – Ve,…

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Q: Find the critical points for the function f(x,y)=96xy−0.75(x+y)4 and classify each as a local…

A: Given Data The function is fx,y=96xy-0.75x+y4.   Differentiate the function fx,y=96xy-0.75x+y4 with…

Q: 1 Let H(s) Using convolution to find h(t) s2 (s-a)

A: Inverse Laplace transferom

Q: Determine the values of constants a, b, c, and d so that f(x) = ax + bx + cx +d has a local maximum…

A: We have to determine the value of a, b, c and d

Q: Let f(x) = (x – 1)² + 4x – 3. Find its critical - number and critical value. If the function has no…

A: We have to find

Q: Find all the critical points of the function and determine at each one whether there is a local…

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Q: + A(- for 0<x< 1, then u attains its maximum in the interval 0 sxs1 either at x=0 or at x= 1.

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Q: Let f (x, y) = y - 8ry + 2x? – 3y + 4x - 23 . Find all critical values for this function and…

A: If rt - s2 &gt; 0 and r&gt;0 then the function is minimum at point ( a,b) If (rt - s2) &lt;0 and…

Q: Given f(x)= x' – rx + k where r E r > 0 and r # 1, and k to be any constant. Prove tha if 0 1, fhas…

A: The given function: Where and k to be any constant. To prove that: If 0&lt;r&lt;1, f has a…

Q: Find a cubic function f(x) = ax + bx2 + cx + d that has a local maximum value of 4 at x = -3 and a…

A: Here we have to find the cubic function that has a local maximum value of 4 at x= -3 and a local…

Q: Suppose that t hours after the injection of x milligrams of adrenalin the response is R units, and…

A: The response after t hours of x mg of adrenalin is R=te-t(c-x)x where c is any constant. We want…

Q: find the formula for a function of the form f(t)=at+b/t with a local minimum at (3,3) and a local…

A: For critical values of f(t), f'(t)=0Critical values of f(t) are t=-3 and t=3So we find f'(t) from…

Q: Suppose the function f(x)=3x^4+ax^3+bx^2 has a critical point at x=2, for which f(2)= −80. Determine…

A: Suppose the function f(x)=3x4+ax3+bx2 has a critical point at x=2, for whichf(2)= −80. Determine a,…

Q: Find a cubic function f (x) = ar + bx2 + cr+ d that has local maximum value of 28 at x = -1 and a…

A: to find:- cubic function f(x), hence the value of a, b, c &amp; d.

Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…

Q: If f(x) has a local maximum at an interior point x= c, then f'(x) exists .a f(x) has a critical…

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Q: For a function f(x.y), suppose that fxx = 2 and D(x,y) = fxxfyy - fxyfxy = 12y - 36. Which is true…

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Q: Find and classify all critical points of the function defined by h(x,y)=x^3−3x+3xy^2.

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Q: Find the absolute minimum and absolute maximum values off on the given interval. f(t)=t√ 25-t²,…

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Q: Given the function z = f(x, y)=x²y+2y² + 4xy-2, find the following: ) Find all of its critical…

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Q: Given a function f(x, y) = x° + y° + 3x² – 18y + 81y + 5 - The function has four critical points in…

A: Consider the given function as fx,y=x3+y3+3x2-18y2+81y+5

Q: 6. Find all the critical points of the function f (x, y) = x2 + 1 + 4xy – 7 and determine whether…

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Q: 1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a…

A: You must have an idea about to how to find relative maximum or minimum using critical points.

Q: Find the critical point of the function, then determine if it is a local maximum, local minimum, or…

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