The function f: R R satisfies the condition mf (x-1)+nf(-x) =21x|+ 1. If f(-2) = 5 and f(1) = 1, then find (m + n).

Q: The function f(x) = 11 – 7x has an absolute maximum value of and this occurs at x equals

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Q: Find the particular solution determined by the given condition 314 f'(x) = 3x -6x; f(1) = -6 II

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Q: The domain of the function f defined by e5x+3y+9xy5 f(x, y)= √130-5x²-5y² is equal to: In D = {(x,…

A: We are given the function all for two variable for which we need to verify if the given set is…

Q: Given k E R, the function f(x, y) = kx² .2 %3D [A) a minimum point, if k = 0 (B) a maximum point, if…

A: Given,  fx,y=kx2+k-1y2+12xy Using second-order partial derivative, check for maxima and minima.

Q: (f) What is the first-order condition implied by unconstrained maximization of I1 X 1333 X, where x…

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Q: The function f(x) = 2x³ – 36x² + 192x - 3 has two critical numbers. The smaller one is x = and the…

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Q: If we use the secant method on f(x) = x+x3+3 with X-2 0 and Xn-1 = 1, then Xn is_

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Q: Find the Critical Numbers of the Function: f(x) (x2 + 6x - 7)2

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Q: Find the particular solution determined by the initial condition. 2/3 f'(x) = 3x - 6x; f(1) = - 7…

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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: Find the critical numbers of the function. a. f(x) = x³ + 6x2 – 15x

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Q: Q1. Find ý of the function x2 – e2x+3y – In(xy³) = 0. -

A: here is the solution

Q: 2. Calculate the point(s) of intersection of f(x) = 2x² + 4x – 11 and g(x) = -3x + 4.

A: Given f(x) = 2x2 + 4x - 11 and g(x) = -3x + 4

Q: Given the function f(x)=x3−2x2−4x+2, find the value of c that satisfies the conclusion of Rolle's…

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Q: Given that f(x) = 3x – 1, g(x) = 2x and h(x) = x + 1, determine: a. hgf(x)  b. hgf(-2

A: Given : f(x) = 3x-1             g(x) = 2x             h(x) = x+1  To Find : hgf(x)…

Q: The linear functions m(x) and n(x) are perpendicular to each other and intersect on the x-axis. If…

A: Two lines with slope m1 and m2 are perpendicular to each other if m1m2=-1 Given: m(x)=4x+48 Let the…

Q: Find the maximum and minimum values of the function f(x) = x² – 6.x +7 on the interval [0, 5].

A: It is given that, f(x)=x2-6x+7   , on the interval 0,5We have to find the maximum and minimum values…

Q: b) f(x) = x2-x %3D x²-1

A: To find out where the function is discontinous.

Q: Find the linear approximation of f(x) = x4 + 3x2 at a = 1.

A: We first find f'(a)=f'(1) f(x)=x4+3x2f'(x)=4x3+6xf'(1)=4(1)3+6(1)f'(1)=4+6=10   We now find f(1).…

Q: (2) GIVEN: f.R- R, Sx) = x²(3x– 1). Find f'(x) in factored form.

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Q: Given f(x) = 3x° + kx – 10, and x – 2 is a factor of f(x), then what is the value -- of k?

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Q: The function f(x) = x²e*- ex has a root in [0,2]

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Q: 3. For the function f (x) = 4x2 – 25, a) find f(-1) - %3D %3D b) find all x when f (x) = 0

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Q: f(x) = 15- (3-t)(r - 8t + 7)

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Q: . The function f(x, y)= 8x' - /4x* + 3y* is homogenous in x and y of degree -. The function f(x, y)=…

A: Here we have to find the degree of homogeneous function

Q: The function f(x) =is 1-z2 Is 9+z2

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Q: Find f'(a) for x2 f(x) = x + 6 at a = 3.

A: Given function :

Q: If g (x) = 3x² + 12x – 96 on the interval [-8, 4]: What value of C satisfies Rolle's theorem?

A: here we have to use the result of the Rolle's theorem.

Q: b. Given f(x) = 3x + 2, g(x) = 2x² – 4x and h(x) = x-x+ 7, find (g + h) (-1/2). %3! %3D

A: Given: f(x)=3x-2, g(x) = 2x2 -4x and h(x) = x2 -x+7 To find: g+hf-12 This can be defined as follows:

Q: Find the Critical number of the function f(x) = -2x^2 + 16x + 7. x = ?

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Q: The function f:R R satisfies the condition mf(x-1)+ nf(-x) =2|x |+ 1. If f(-2) = 5 and f(1) =1, then…

A: Introduction :Given ,function f: R->R Which satisfies the condition mf(x-1) - nf(-x) = 2|x| +…

Q: Q 2/ find the value of (k) to continue the function (Vx+1-V2x f(x)= x2-x x = 1.

A: For continuity of function  Lim of f(x) at x=1 should be equal to k

Q: The critical points of the function f(z) = 9x² - 8x + 16 are

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Q: Find a and b so that the function 2.3 – 5x² + 2, x -2 f(x) = ax + b, is both continuous and…

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Q: The function f(x) = 2x³ – 27x2 + 48x – 3 has two critical numbers. - The smaller one is x = and the…

A: We have to find critical numbers for the function: fx=2x3-27x2+48x-3 We know that critical points of…

Q: The function f(x) = 2x 30x2 + 54x – 7 has two critical numbers. - he smaller one is x = nd the…

A: Given query is to find the critical value of the function.

Q: 3. For f(x) = x - 10, find the solution to f(x) = 5.

A: f(x) = x - 10 f(x) = 5

Q: = x, find (f o g-3). Given that f(x)=2x+3 and g(x) (fo gX-3)-

A: (fog)(-3)=f(g(-3))

Q: Find a number c that satisfies the conclusion for f(x) = x + x-1 on the interval [0, 2]

A: Answer is 2/√3

Q: Find the range of f{x}=x² +5x+6. O (00, 0) O (o, -1/4] O -1/4, )

A: Topic = Functions

Q: Find the critical numbers of the function. a. f(x) = x3 + 6x? – 15x b. g(x) = V1- x2

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Q: Given that f(x) = 2x-2n + 8x², what value should be assigned to n to make f a function of degree 3?

A: Given f(x)=2x-2n+8x2. We need to find what value of n makes f(x) a function of degree 3.

Q: Suppose z is a function of x and y, and z^xe^6y=y2+x2. Solve for ∂z/∂x and ∂z/∂y. [b]

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Q: The function f(x) = 2x + 6x² – 5x + 1 is concave downward on the interval None (-0, –1) (-0, c0)…

A: Concavity.

Q: 3- For what value of c is the function continuous? Provide a well- communicated solution. F(x) = {…

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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: Given the function f(n)=2n^4+4n^3−6n^2 its f-intercept is : its n-intercepts are :

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Q: Find f (x) given f "(x)= 6x² +8x³ – x and the initial condition f(-1)=- 2

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Q: The critical point(s) of the function z= 2x²-4xy-2y²+3x-7y+6 is/are...

A: In this question, we need to find the critical points of the function z = 2x2-4xy-2y2+3x-7y+6.