2. If f(x) = kx' +x² – kx+2, find k such that the graph of f contains the point (2, 12).

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives and fz = 44,…

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Q: = x2 - 4x + 1 with domain [0, 3] f has ---Select--- v at (x, y) = f has ---Select--- v at (x, y) = f…

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Q: The function f..) = x+x +3x- 1+2r,x + 2 defined on R has ohly one stationary point. Show that it is…

A:

Q: 8. Find the maximum and minimum values of f(x) = x+ x - 2 on the interval [- 2, 2]. 9. Find the…

A: Please refer the attached image for complete solution.

Q: り If X~メ (2)、 Find the 32-moment of x about zero

A: Introduction: The random variable X has a chi-squared distribution with 2 degrees of freedom, that…

Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: Find the orthogonal trajectories to the family of curves: x² = C-v'(ln y² –1).

A:

Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval. y = √x, [9,…

A:

Q: 2. Compute F-dr where E= (x+ y,x-2z,z- y) and curve C is the line segment from (-3,5,1) C to…

A: Using line segment as the base of a rectangle, we choose the height to be the height of the surface…

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

A:

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: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

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

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: . How many point(s) of inflection are on che graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x² -…

A:

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

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Q: Is ƒ(x, y) = x2 - xy + y2 - 3 more sensitive to changes in x or to changes in y when it is near the…

A: Partial derivative of f w.r.t a variable is the indicator of the sensitivity of f towards that…

Q: Determine two functions, defined on the interval  ( − ∞ , ∞ ) , whose Wronskian is given by  W ( f 1…

A: To determine two functions having the prescribed Wronskian and decide on their linear independence

Q: Find the slope of the curve y=x2−3x−4 at the point ​P(2​,−6​) by finding the limiting value of the…

A: Giveny= x2-3x-4 = f(x)at point ( 2, -6)as f(x) =x2-3x-yand f(2+h) = (2+h)2-3(x+h) -4…

Q: 9. Find the local minimum and local maximum values using both the First and Second Derivative…

A: To find the local minimum and local maximum values.

Q: 7  please answer, type the solution if you can please. or write clearly

A:

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

A:

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 and the line tangent to y=gx at x=5 is y=6x-27. Consider,…

Q: Q4: Find and classify all critical points for the function: z2 = (x3/3)-(y3/3)+2xy

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Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: The tangent line to y = f(x) at (-1,-8) passes through the point (-7,5). Compute the following a.)…

A: The tangent line to y=f(x) at (-1,-8) passes through the point (-7,5)

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: Points at which fx = fy = 0 are called critical points.

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

A:

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: (5) Use the first derivative test to classify the critical numbers of the function s(r) = 2¹-4r³+17.…

A:

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: Q2: Find all critical numbers of the function f(x) = (x- 2)2/3 +1 and classify each critical point…

A: Here we will find out the required value.

Q: (5) Find the curve y = f(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

A:

Q: ,2 Let f(x) = x – 12x -27x + 1. Find the critical points of f(x).

A: Find the derivative as follows: f'x=ddxx3-12x2-27x+1        =3x2-24x-27

Q: Suppose the graph of f(x) = x3is compressedvertically using a factor of 1/3and then shifted to…

A: Given : The parent function is f(x ) = x3 . The graph of f(x) = x3 is compressed vertically using a…

Q: Find the global minimum of the function f (x) = 1+x² on the interval (-∞, 0) . Write DNE is there is…

A:

Q: Consider f(x) = xlnx on the interval [1,6]. When will the first derivative equal zero? For each…

A: Given that: f(x) = xlnx   x∈[1,6] To find: When will the first derivative  equal to zero. And for…

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives. In each case,…

A:

Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: 8) State the critical points of the function k(x) = x2 In x2.

A: Given,          The function kx=x2lnx2

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

A:

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 coordinates of the critical point according to the criterion of the first derivative of the…

A:

Q: 4) Let g(x,y) = 2x² + y² – x²y. a. Find the critical point(s) of g. b. Use the second derivative…

A:

Q: Suppose that a function f(x,y) has a critical point at (2,3). Given that fæx (2, 3) = -4, fæy(2,3) =…

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x3, [−4,…

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Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: If f(x) = x² + k find k so that f has a critical number at x = 3. %3D

A: To find the critical number for any function fx we have to solve the derivative f'x=0. That is we…