Determine the linearization of the function f ( X) = (√4X+ 1)  at x=6. Use that linearization to approximate the value of √25.2.

Q: Find the first and second derivatives of the functions in Exercises ( E q² +3 12q

A: We know that; The Power law: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g' The Quotient rule:…

Q: Find the average rate of change of f(x)=3x2 +2x−2 on the interval [2,t].

A: Consider the function f ( x ) on the interval [ 2,t ],

Q: dP dt т 1- kP 1- M

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Q: Find the derivative of the function. (S h(x) = %3D 8x2 + 9

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Q: ६(६+६) : (11-2+21) 2 (5+276 : (7 (622) 7) *b - (b) 4 (+) दहिका xb SEX K xb

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Q: 1. Find the derivative using chain rule. (a) f(x) = (x5 – 2)20 %3D Answer: (b) f(x) = V3r² + 1 %3D…

A: Since you have posted a question with multiple sub parts, we will solve the first three subparts for…

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 derivative of the function.

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Q: Find the derivative of the function. A y = 7tan-(x - V1 + x²) %3D (2* * I^ -

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Q: Find the linearization of the function F(X) =sqrt (x+3) at a= 1 and use it to approximate the…

A: Therefore linearization at a = 1 is,

Q: Find the derivative of the given function from the first principle ax2+bx+c

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Q: Find the derivative using the definition. a. f(t) 2t+1 b. g(x) = 2x² +1

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Q: Consider the function below. Approximate f(1.99) using a linear approximation. f(x) = 2x³ – 4x² – 3…

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Q: The derivative of the function f (x) = (x-1 – 2)(3 – Vx) is,

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Q: Find the first derivative of Select the correct response: 4x 9y –4x gy 2 4x² +9y² = 36. 9y 4x -gy 4x

A: Solution :  Given equation of ellipse is  4x^2 + 9y^2 = 36 Differentiating with respect to x we get…

Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 & f/0=e0=1

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

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Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (2) — 5а — 4 %3D | 2. f…

A: Recall: Derivative using Four step Rule:step 1 : Write f(x+h) and f(x).step 2 : Compute f(x+h)-f(x)…

Q: Let f(x,y)=x² - 2y² + 3x. In what direction from (2, –1) should we proceed so that the change in f…

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Q: If L(x)=mx+b is the linearization of the principal square root function of x at x=900, then b= Use…

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Q: Q2: - Find the second derivative of the following function at x = 2 15 marks 1) y=+ V 2) y 3 (x +)…

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Q: 1- at 9=0

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Q: What is the derivative of the function f(x)= In(3x2) ? а. f'(x)= 2 b. None of these. с. 1 f'(x)= %3D…

A: We have given that  The function is f(x) = ln(3x2)

Q: Find the first and second derivatives of the function. f(x) = (7x² + 6)7/2 r'(M) = | 49x(7x² + 6)…

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Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: Where is the function y =4x/x-3 concave downward? Show mathematical work to clearly answer this…

A: For a given function y=f(x) the curve is concave downward in an interval I when the second…

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: 2. Find the derivative using chain rule. (a) f(x) = 5(2.r + 3)3 Answer: (b) f(x) = (x - 4)*(2x +3)…

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Q: Find the streamlines corresponding to: f(z) = z²

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Q: Find the indicated derivative.dp/dqfor p =q2 + 2/4q-2

A: Given a function in p in terms of q as shown below. We need to compute dp/dq.Here we use (u/v) rule…

Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

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Q: Find the derivative of the following using the three-step rule Зх-1 1. у3D 2x+5 2. y=Va² +x²

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Q: Find the second derivative of f (x) if ƒ (x) = (2x + 3)* %3D A) 4(2x + 3)³ (B) 8(2x + 3)3 (C) 12(2x…

A: Proceed as shown...

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: Use the chain rule to find the derivative of f(x) = 2(10r° + 9®)™ You do not need to expand out your…

A: Given: f(x)=210x8+9x615

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: Find the derivative of f (a) = e" (x² + 2).

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Q: Find the derivative of the function m: f(x)= e^x^3+4

A: Topic = Derivative

Q: arke

A: please refer to the image below

Q: C. Apply the chain rule to find the derivative 1. y = (8 - 3x )3 3. y = (1-x)7 2. y = V2x + 1

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Q: Use the limit definition to calculate the derivative of the linear function. g(t) = 8 − 3t

A: Plug the given function in the limit definition

Q: Find the derivative of the function C=25(11q^5−14)^8.

A: According to the differentiation rule the power comes down and reduces by one and then chain rule is…

Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

Q: Use this definition to compute the derivative of the function at the given value. h(x) = 5x² + 1 X =…

A: We have to find derivative

Q: 3) Use the definition to find the derivative of f(t) = +1 t+1 %3D

A: f'(t) = -1/t2

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

A: 555

Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Let L(x) be the linearization of the cube root function at x=64. When using L(x) to approximate the…

A: The linearization L(x) for tge function f(x) at x =a is given as L(x) = f'(a) (x-a) + f(a)

Q: Let f(x,y) x2-2y² +3x. In what direction from (1,2) should we proceed so that the change in f in…

A: A function f(x,y) from a point increases most rapidly in the direction of its gradient at that…