Let f(x) = Using the centered 3-point formula for 1st derivatives: %3D (x+1)3 f'(0) -0.502509 using h = 0.1 f'(0) -0.500626 using h = 0.05 Applying Richardson's extrapolation on the above values, we get a better approximation of f'(0) which is: O -1.99985 O 0.249999 O -0.499998 O 0.234256

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: Using the forward difference and values of h=0.1, to approximate the derivative of cos(x) at…

A: This is a problem of Numerical Analysis.

Q: .3 Find the derivative of the function f(s)= 12s³+ 5secs. a. f'(s)=36s² + 5secs · tans b. f'(s)= 3s²…

A: We have to find derivative

Q: Let f (x) = Using the centered 3-point formula for 1* derivatives: (x+1)2 f'(0) -2.04061 using h =…

A: given fx=1x+12 f'0≈-2.04061 using h=0.1f'0≈-2.01004 using h=0.05 according to richardson's…

Q: 1) Use forward and backward difference approximations with error of O(h²) and a centered difference…

A: Given function  fx = x2 e-3x7 Step size h =0.2

Q: Let f (x) = (x+1)3 Using the centered 3-point formula for 1st derivatives: %3D f'(0) -0.502509 using…

A: At h= 0.1, f'(0) is approximately -0.502509At h= 0.05, f'(0) is approximately -0.500626

Q: Use the quotient rule to find the derivative. 2.1 +6 f(x) = x2.0 + 1 2.6 3.7 +2.1x x1.1 - 15.6x 1.6…

A: You need to just apply quotient rule.

Q: Consider the function on the interval (0, 2). Use a graphing utility to confirm your answers for…

A: Let f(x) be a real valued function,  then The critical points occur at f'(x)=0 .If x∈I,f′(x)>0 ,…

Q: Let f(x) = Using the centered 3-point formula for 1t derivatives: %3D (x-2) f'(0) 0.251255 using h =…

A: According to the Richardson's extrapolation formula, the true value of the derivative at any point x…

Q: Let f (x) = (x+1)= Using the centered 3-point formula for 1st derivatives: f'(0) & –0.502509 using h…

A: Solution:

Q: Let f(x) = Using the centered 3-point formula for 1st derivatives: %3D (x-2): f'(0) & 0.251255 using…

A: Solution:

Q: Use forward and backward difference approximations of O (h) and a centered difference approximation…

A: Given : fx=sin0.5xx , x=1.5 , h=0.2To Find: The first derivative by using forward, backward, and…

Q: Let f(x) = (x-2)³. Using the centered 3-point formula for 1st derivatives: f'(0) 12.01 using h = 0.1…

A: As per the question we are given the 3-point approximation of the first derivative of the function…

Q: Let f(x) = 2 Using the centered 3-point formula for 1 derivatives: (x+1) f'(0) -0.502509 using h =…

A: According to Richardson's extrapolation formula,  the better approximate value of the derivative of…

Q: Consider the function f(x), whose first and second derivatives are given below: 26 8x27 208x(x-54) =…

A:

Q: Estimate the true percent relative error for the first derivative of the function, y =[en(x)]², at x…

A: We can solve this using Central difference formula f'(x) = (f(x+h) - f(x-h))/(2h)     x 0.95 1…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

A:

Q: Let f (x) = Using the centered 3-point formula for 1st derivatives: (x+1)= f'(0) -0.502509 using h =…

A: Solution:                        f(x) = 2x+12Using the centered 3-point formula for 1st…

Q: Shown below is the graph of f'(x), the derivative of the continuous function f(x) defined on (0,6).…

A: