Show directly that the given functions are linearly dependent on the real line. That​ is, find a nontrivial linear combination of the following functions that vanishes identically. f(x)=5x, g(x)=6x^2, h(x)=6x-24^2   enter the non-trivial linear combination. (36)5x+ (     ) 6x^2+ (    ) (6x-24x^2)=0

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: Determine the equation of the quartic function with the following characteristics x-intercepts at x…

A:

Q: Find the critical numbers of the function.   f(x)  = 2x3 + x2 + 2x

A: We find the first derivative using the power rule

Q: Find the constant a such that the function is continuous on the entire real line. Ax) = {2x2, (ах -…

A: Given that , the functionfx=2x2,x≥1ax-7,x<1We have to find constant a such that the function is…

Q: Determine whether there exists a constant c such that the line x + cy = 1: passes through (3, 1).

A: We have to determine the value of constant c such that the line x+cy=1 is passing through the point…

Q: Find the linearization of the function at a . f(x) = x 4 + 3 x2    , a = -1

A: We know that ,The linearization of the function at v=ais given by fa+f'ax-a

Q: If f (x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule %3| multiplies…

A: It is given fx=x4, gx=x3, f'(x)=4x3 and g'(x)=3x2.

Q: 2-→Find-the-residues of the-function-at-its-poles F1:(2)-(2-z-+3)/(z²-4)1

A: The given complex function is: F1(z)=2z+3z2-4

Q: Determine all critical points for the function. 5) y = 3x2 - 96x

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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: Suppose that the marginal-revenue function for a manufacturer's product is (dr/dq) = 100-(3/2)q2 ,…

A: Given,          The marginal-revenue function for a manufacturer's product is drdq=100-32q2,…

Q: You will calculate L5 and U5 for the quadratic function y 2² + z + 14 between z = 0 and z = 2. Enter…

A: To solve the following problem

Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: Find all critical points of the function: f (x) = 7x − 2

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Q: Differentiate the following functions using Chain Rule: 1. y = (4x + 3)² 2. y = √5x-2 3. y = (6x-4)²…

A:

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: One of the two tables below shows data that can best be modeled by a linear function, and the other…

A: First compute the first order and second order difference in given table: since the successive…

Q: Goes through (0, -2) and has a local maximum at (1, 3) f(x) = 5x² - 10x - 2 O B) f(x) = -5x² + 10x +…

A:

Q: A consultant advises the owners of a beauty salon that their profit p each month can be modeled by…

A: The profit p(x)=-50x2+3500x-2500

Q: I. Differentiate each function using chain rule. 1. y (2x3 + 1)5 2. y=x² + (4x5 – 5)3 3. y = (-2b8 +…

A:

Q: Find the critical numbers of the function.…

A: Critical numbers : f(x)=4x2-6x The derivative of the function is f'(x)

Q: Find the linearization of the function at x = 1.* f (x) 2x - 3x + 7 %3D

A: From the given problem:   fx=2x3-3x+7 ; x=1   As we know that the expression for linear…

Q: Suppose (0, 2) is a critical point of a function, with continuous second derivatives. In each case,…

A:

Q: Determine all critical points for the function. 2) f(x) = 45x3 - 3x5 %3D

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

Q: Find the critical points for f(x) = 3x5 - 20x3. %3D

A:

Q: At what points are the functions continuous x+3 y =- 3x, Зх, y = y = (2x – 1)3 х-2 x2 -3x-10'

A: To find the points where following functions are continuous y=1x-2-3xy=x+3x2-3x-10y=2x-113

Q: Find all critical points of the function f(x) 3x 5x2-2x+14

A:

Q: Find a function whose graph passes through the point (1,2/e) and satisfies x^2y'=y.

A: Given differential equation     x2y'=y   and initial condition  at x=1,y=2/e

Q: f(x) = x3 + 5x² + 2x

A: Given: f(x)=x3+5x2+2x

Q: Show solution/process. 1. f(x) = 2x² – 4x + 5 at the point (–1,11) 2. f(x) = v25 – x² at the point…

A: Since there are more than one question, only one question can be answered. The function is given by,…

Q: Find a formula for the linear function with slope −3 and x-intercept 2.

A: Refer to the question.For the linear function with slope −3 and x-intercept 2, use the slope…

Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

A:

Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

A:

Q: + 2x if xs -1 if -1 1 f(-4), f(-}). (-1), f(0), f(25)

A:

Q: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?

A:

Q: Determine all the critical points for the function y = Vx² (2t- 1)

A: Given function is in two variables x and t For critical points we calculate Partial derivatives…

Q: Find the critical point(s) of the function f(x) = x³ + x−³+2.

A:

Q: 8(x) = X -x3 + 2x x4

A:

Q: If the utility or profit function for a product is: U (x) = 5,600x + 85x ^ 2-x ^ 3-200,000 dollars,…

A: If the utility or profit function for a product is Ux=5600x+85x2-x3-200,000 dollars, will selling…

Q: Examine whether or not the function fx' - 2r +1 ifxs 2 S (x)= x'-2r +1 [3x-2 if x>2 Is continuous at…

A: Given function, fx=x3-2x+1,     if x≤23x-2,            if x&gt;2 To find the continuity of the…

Q: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: Suppose that f is a linear function with slope 2.4 and that f(5) = -1. What value of x gives f(x) =…

A: Consider a linear function f with slope 2.4 and f(5)=-1 .

Q: find the marginal revenue of the function. Using the quotient rule.  40x^2 -20x/x^2-10-2

A: Given: Revenue FunctionRx=40x2-20xx2-10-2 To Find: Marginal Revenue Concept: a. Marginal RevenueMx…

Q: Find all critical points of the function f(x) = 4x² 3x²-2x+12

A: Here we have to find the critical points.

Q: Find the critical numbers of the function. f(x)=32x-2x^2 x=

A:

Q: Over the next 20 years, a company projects its continuous flow of revenue to be R(x) = 100e01z…

A: Consider the provided question,

Q: If f(x)=x* and g(x)= x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule multiplies derivatives to…

A:

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

A:

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.