The linear approximation of the function f (x) =90– 55x at x=2 is: 90-55x -20+55x 110+55x 110-55x

Q: Find the average rate of change of the function f(x) = 2x² + 16x + 28 on the interval [-3, –3 + h].

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Q: Find the linearization of the function f(x) = x^8 at x = 1

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Q: Given that f(3) -2 and f'(3) = 4, estimate f(3.5) using a linear approximation.

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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: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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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 absolute maximum and absolute minimum of the function f(z) = z² – 6z + 5 over (1,

A: Given: fx=x2-6x+5, 1,6

Q: Given f(X)=−xe^x whats the root of the linearization of f(x) at a = 4.3?

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Q: Find a formula for the linear function f(x) with slope 2 and vertical intercept 1. f(x) =

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Q: Find the maximum and minimum values of the 2x3 function f(x,y) = * - 2xy – 5x + 2y² + 4y + – 2xy –…

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Q: Determine the linearization of the function f ( X) = (√4X+ 1)  at x=6. Use that linearization to…

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Q: Find the linearisation of f(x) = 4√x at a = 16. Use this to estimate 4√ 15

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Q: 9.03 6. Vse the linear anproximation of the function (x)= V9-x at a = 0 to approximate the number

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Q: Find the zero of the linear function  f(x)= x+4

A: fx=x+4

Q: Find the average rate of change of the function f(x) = x2-40x+28 over the interval [10, 50].

A: topic - average rate of change of function over interval

Q: Find the relative maxima and minima of y by the second-derivative test: (a) y = -2x2 + 8x = 25…

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Q: Determine the linear approximation for 2√x at x = 5. Use the linear approximation to approximate the…

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Q: Find the linearization of the function at a . f(x) =  x3/4    , a = 16

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Q: Find the linear approximation of the function below at r = -1 and use it to approximate f(-0.8). -7x…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: The population density of a city is given by P(x,y) = - 25x - 30y + 500x + 240y + 180, where x and y…

A: Population density is given by following function  P(x, y) = - 25x2 - 30y2 +500x + 240y + 180

Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

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Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: Find the linearization L(x)  of the function f(x)=x^3/4  at x=16

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Q: for f(x)=2x4-5x3+7 find all potential points of inflection and map the intervals where the function…

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Q: The function f(x,y) = 3x2 - 2xy + y2 + 8y has one stationary point. What is the location and…

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Q: 1- at 9=0

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Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: -2 Write the equation for the linear approximation of g(x) = In(vr² +5) based at x =-2. Justify your…

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Q: Find the point at which the line f(x) = - x – 2 intersects the line g(x) 3x + 6 %3D

A: f(x) = g(x) Thus, -x-2 = 3x + 6   Separate variables to LHS and constants to RHS -x-3x = 6 + 2 -4x =…

Q: Find the average rate of change of the function f(x) = −x2 + 8x − 4,from x1=0 to x2=4.

A: The average rate of change of f(x) on the interval [a,b] is f(b)−f(a)b−a we have that a=0  , b=4 ,…

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: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: Find the linear approximation to the following functions at the given point a. ƒ(x) = 4x2 + x; a = 1

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Q: Find the linearization of the function f(x) = 1/(9x+8) at x = -1.

A: Topic : function

Q: given the function f(x)=axln(x+b), where function is decreasing at x=1-b?

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Q: Produce the linear approximation of the given function at the specified value. f(x) = sqrt(x); x =…

A: fx=x,  x=2 Differentiating with respect to x, we get f'x=12x Now at x=2, f2=2  &  f'2=122

Q: At what value of x does the local max of f(x) occur?

A: Given, fx=∫0xt2-491+cos2tdt

Q: Given the function f(x) = -x² – 7x + 19, determine the average rate of change of the function over…

A: Given function is: fx=-x2-7x+19 And the given interval is: -9≤x≤3 At x=-9:…

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x + 3y = 10.

A: Solution of given question is written in below steps.

Q: The function f(x, y) = -2x² + 4y² - 12 has a local maximum at the point (0,0). Select one: O True…

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Q: Given the function g(x) = -x² + 6x + 11, determine the average rate of change of the function over…

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Q: find the critical point and classify the function f(x,y) =xlny +x2 -4x-5y+8

A: Answer

Q: Find the approximate value of the function f(x)=√5x−1 at x=1,99.

A: Given Here a = 2. The formula for approximate value is Substitute a = 2 in given function to get…

Q: Given the function f(x) = -x² – 7x + 15, determine the average rate of change of the function over…

A: Given, fx=-x2-7x+15 over the interval -9≤x≤3 To find the average rate of change.

Q: Given the function h(x) = -x² – 6x + 11, determine the average rate of change of the function bver…

A: The average rate of change of a function, y=f(x) over the interval, a, b is calculated using the…

Q: Find the linearization of the function at the given point f(x,y)=-10x+8y-9 at (-7,4). A.…

A: I have appended the formula used in the solution part

Q: The derivative of the function f(x) = 18 is 1 5x 18 5x + 18 18 5x4 + (x) 18 5x4 (교2) 18 5x4 + (23)

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Q: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

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Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?

A: average rate fo change in an interval (a,b) =f(b)-f(a)b-a