Find a good numerical approximation to F(4) for the function with the properties that F'(x) = e-x+15 and F(0) = 1.

Q: 3. Given the equation y = x³ - 3x² + 3, determine all Critical Points and classify using the SECOND…

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Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 1. y Arctan- 3-V9-x2 2. y= 4 Arccos +…

A: 1.   From the given problem:   y=Arctanx3-9-x2   As we know:   d2ydx2=ddxdydx   So,…

Q: Solve the first derivative of f(x) = e-2x In x at x 0.5 using forward finite-divided difference and…

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

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

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Q: When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .

A: Given Data The function is f(x,y)=3xy²-xᶟ.   Differentiate the function f(x,y)=3xy²-xᶟ with respect…

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORN 3x-4 1. y = Arctan 2. y = 2 Arccos (1…

A: y=Arctan3x-44

Q: Calculate differential: f (x) = = e-* cos(3x) + 2 of the range [1,2] with h=0.05 a) Using the…

A: Equation is f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of the…

Q: 3. Solve the first derivative of f(x) = evx at x = 0.5 using centered finite-divided difference and…

A: To find the first derivative of f(x) at x=0.5 using centered finite-divided difference and a step…

Q: Find the critical points/number of the function h(x) = e^x sinx-sinx+cosx by applying derivatives.

A: First calculate its derivate then equate it equal to 0 to obtain the critical points. h(x)=exsin…

Q: Find the derivative of the function. rcos(x) y = In(1+2t)dt sin(x)

A: Applying Leibniz rule

Q: Find the global maximum and minimum of the function on the given…

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Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

Q: Solve the first derivative of f(x) = 52x+1 at x = 0.5 using backward finite-divided difference and a…

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Q: y = (Arccos 3x³)³

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Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: Find the derivative of the function. f(x): f(x) = 2xarccos(x) – 2/1 – x² 2arccos(x) + 2 2arc cos (x)…

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Q: Find the second derivative of f(x) = x2+ e* - COSX. O a. f(x) = 2x + xex - cosx O b. f'(x) = 2x + e*…

A: Solve by derivative

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

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Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: 9 Derivative of fi») 1x 4 . 5. 1 f) 1x1cosx, fird f'n)

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Q: Compute the indicated derivative using the chain rule. X = 4 + 3t, y = -7t; Oy

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Q: What is the 4th derivative at x = 0 of the function f(z) = (2r + 1)* %3D

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Q: 6. Find the first order derivative with respect to z of the function u = In/x2 + y2 +z²

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Q: Compute the second derivative of f(x)=ex+x at x = 1 using a step size h = 0.2

A: To find the second derivative of f at x = 1. The approximation formula for second derivative at a…

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

Q: What is the value of the first order derivative of the closed function given as…

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Q: 5. Find the first order derivative with respect to y of the function U = In/x² + y² + z²

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Q: Find the weak derivative of f() = |x² – x + 1/5| on the 1) interval (0,1).

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Q: 1- Solve the second derivative forf(x, y,z) = e sinay3) əx2

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Q: What is the approximate value of the first derivative of S(x)=-0.1x*-0. 15x-0.5x-0.25x-1. 2 at…

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Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

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Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

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Q: Approximate the derivative of f(x)-x3+4x2-10x+5=0 at x=3 using the forward, backward and central…

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Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: 1. Solve the first derivative of f(x) = e-2x In x at x = 0.5 using forward finite-divided difference…

A: To find the first derivative of the function f(x) = e-2xlnx at x = 0.5 using forward finite-divided…

Q: 4. F(x) = (1-t) dt

A: To find the first derivative

Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

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Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – /cos(x) (2n 4+v3 3' 2v3 At the…

A: Given: f(x) = 1 + csc(x) -cos(x)   To determine: Equation  of the tangent line at the point…

Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

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Q: (a) By using the chain rule and the derivative (1, if x>0 4 (1xl) ={-1, if x<0 %3D find (lx-x) vxE…

A: Use the chain rule to differentiate the above given function and than use the given derivative of…

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Consider the following function: fx=x2+2x Differentiate fx with respect to x: ddxfx=ddxx2+2xf'x=2x+2

Q: The function whose derivative is given by f'(x)=(x-¹), x 2. What is the #+2 critical point of f?

A: Critical point of a function is a point where either the derivative of function is zero or not…

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: Find the derivative of the function. (x-7)(x²+2x) +3 y = O A. OB. dy dx O D. dy dx dy O C. dx dy dx…

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