14. For the function f(x)=ax³+bx² –5x+9 , determine the values of a and b so that s(-1)=12 and f'(-1)=3 .

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

Q: 20. The fourth derivative of y = Jx -1 is 8 D.-은(x-1) 2 16 15 A. -(x – 1) В.- С.- 8. (X - 16 M| 00

A: This question is related to differentiation, we will use basic differention rules and results to…

Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: 1.If f(x,y) cos(4x-2y)+ln(y² -2x) find £xy fx fxy,

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Q: Find the second derivative of the function f(x) = 2 – 3x + 5æ/2 – 7e" . 15 f"(x) = –3+ 2 7e" f" (x)…

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Q: 8. the second derivative of f(x) =3e^5x , is а. 15е^5х b. 125e^5x с. Зе^5x d. none of the other…

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Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

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Q: 18 The derivative of the function f(x) = x² + is 18 4x3 + (æ³) 18 O 4x³ - (æ²) 18 4x° + (x) 4x + 18…

A: d/dx(xn)=nxn-1 Given f(x)=x4+18/x  To find the derivative of f(x) differentiate once

Q: Suppose F(r, y) is a C' function such that F(0, 0) = 0. What conditions on F will guarantee that the…

A: Let us consider, F^(x,y)=F(F(x,y),y)  On applying the implicit function theorem , can get a solution…

Q: The second derivative , for the function 7y+ 13z 3a2 is O y = 9

A: Given query is to find the second derivative of the function.

Q: 2²y. 3. Consider the function f(, y) =

A:

Q: 4. Find f'(x), if f(x) = (2x – 8x²)-²(3x + 1). 5. If y is a twice differentiable function and x cos…

A: Differential equation. Solving only first ques as per bartleby guidelines.

Q: 5. If f(x)= 5x² + 2x+1 is an invertible function, find the slope of the tangent line to f^(x) at the…

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Q: if f'f′ is the derivativeof ff with 2∫1f'(x)dx=10∫12f′(x)dx=10 and f(2)=4,f(2)=4, then f(1)

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Q: Find the second derivatives:y^n for y=1/8x^4-1/3x^3+3/4x^2-3x+5 And f(x)=2x/5x-2

A: (i): Given : y=18x4-13x3+34x2-3x+5 f(x)=2x5x-2…

Q: Find the second derivative of the function y=x(x² – 1) (А) 4x(5х2 - 3) в) 2x(5x2 - 6) (с) (2х -…

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Q: 8. Compute the derivative of the following equation. (1) y = (x +1)3(2x – 2)2 (ii) y2-4x² y+x=16

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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: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: The derivative of y= (V x - 2 )(Vx+1) is equal to: х - 1 A 2x+1/x-2 2х-1 B Jx+1/x=2 2х-2 2/x+1/x-2 D…

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Q: [Q2] For the following function Ax)= (2* /x) 1- Obtain the first and the second derivatives for x =1…

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Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

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Q: x and y are functions of a third variable t. If √√x + √= 5 and dt = 2, find when = dt 1

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Q: = x³y² – 3x²y + 5x – 3y + 12

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Q: 27. The first derivative of y = is (4x+1) -24 b. 24 C. -6 6. (4x + 1)+ (4x + 1)+ (4x + 1)4 (4x + 1)*…

A: y=-2(4x+1)3

Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

A:

Q: find the solution of following derivative by Runge-Kutta method f(x,y) = -2x3+ 12x2 - 20x + 8.5 let…

A: Consider an initial value problem dydx=f(x,y) with the initial condition yx0=y0. Then Runge-Kutta…

Q: 11. If f(r) = rª and g(r) = r³, then f' (x) = 4x³ and gʻ(x) = 3x². The Chain Rule multiplies…

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Q: 1. If F(x)= = ² e²² et² dt, find F(1) and F'(x). ez

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Q: 5 What is the derivative of5a2 + 10x + ? A None of the given choices B 10x + 10 + 3x2 10a4 + 10a³ –…

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Q: The antiderivative of the function 4 .3 + 10x³ is, 4 f(x) - -4 .3 + 2.5x³ + c 4 -10 + 1.0xª + c -4 +…

A: According to question given f(x)=44.3+10x3We have to calculate the antiderivative

Q: 1. Find the derivative of the following. f(x)=13x* –7x³+5x²+11x+75 b. S(x)-(x*+2x*+4)(x"-3) 3x -6x+7…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

Q: Suppose m and b are constants. What is the linearization of the function f(x) = mx + b at any given…

A: The given function is: f(x)=mx+bSo,f'(x)=m

Q: Supposed that z is defined implicitly as a function of x and y by the equation x2 + y2 +z2 = 4. Find…

A: The given data is: x2+y2+z2=4 To find the value of dzdx

Q: x² + y² F(x, y) =- - is a homogeneous function of degree

A: For finding degree of homogeneous function, Put x=hx and y=hy

Q: In(4x Given f(x) = the derivative f'(x) is 4 1 4x 1 4x O 4 O z4z

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Q: In (4x+7) 1. Find the derivative of f(x) 5x e 10-18 x? Evaluate the integral: 5x-3x 5 6x*-3x?…

A: Please see the explanation below

Q: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of rapid increase.

Q: (x3-x)² .3. 2 5. у 3 х+1

A: We’ll answer the 5th question since we answer only one question at a time. Please submit a new…

Q: 3. If f(x) = [ v19 +r² dt , find f'(3).

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Q: 7 For the function eX, the linear approximation around x = 2 is %3D

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

A: The given function u=3x4+4

Q: Find the most general antiderivative of f(x) = -10x – (1 – x²)-1/2, where -1< x < 1.

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Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

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Q: Find a function f(x) whose linearization would help me come up with an approximation to 4 26

A: We want to find the function,  It's form is ,L(x) = f(a) + f'(a) (x-a)  We approximate 4/26 ~ 4/25…

Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

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Q: Find the antiderivative of the function: f(x) = ex + 3x - x2

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Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

A: