A car traveling along a straight road is clocked at a number of points. The data from the observations are given in the following table, where the time is in seconds, the distance is in feet, and the speed is in feet per second.   Use a Divided difference scheme to predict the position of the car and its speed when t = 10s. Use the derivative of the polynomial to determine whether the car ever exceeds a 55 mi/h speed limit on the road. If so, what is the first time the car exceeds this speed? What is the predicted maximum speed for the car using appropriate coding scheme?

Q: Find the interpolating polynomial of the following points or functions using Newton's

A: Given: The points -2, 2, -1, -2, 1, 3 and 3, -3. To find: Interpolating polynomial.

Q: Write the Lagrange polynomial for the data X;0 2/3 | 1 Yi 1 0.5 | 0

A: Consider the data

Q: Find the derivative if w=(2x-7)-1(x+5)

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Q: Find the equation of the tangent line to the functions: 1. f(x)= x4-3x3+5x2-2x-1 at x=-1

A: We are supposed to solve only one question. please repost  the remainingquestion separately.To find…

Q: Use the product rule to find the derivative of the following. y = (4x2 + 5) (3x - 2)

A: We have given function y=4x2+53x-2

Q: Find the derivative of the function, using the product rule, then by multiplying each function out…

A:

Q: If , f(x) = Sqrt(x^3-6x+12) at x = 1, then what is the derivative of  f at x=1? Round to the nearest…

A: Given that, f(x)=x3-6x+12 We have to find the derivative of the function at x=1

Q: In  the given question as follows , approximate the function at the given value of x, using the…

A: We have to approximate the function at the given value of x: fx=e4x,      f14 To find f14 we need to…

Q: Find the derivative of the function using the power rule. (a) f(x) = 3/5x5 − 4x −4/3x-3 (b) f(x) =…

A: a) f(x)=35x5-4x-43x-3 f'(x)=ddx35x5-4x-43x-3       =35ddx1x5-4ddxx-43ddx1x-3…

Q: Find the derivative of the function. Simplify and express the answer using positive exponents only.…

A:

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative. y = x3 -…

A:

Q: In the given question as follows , find the nth Maclaurin polynomial for the function:- f (x) =…

A: Maclaurin series is a special case of Taylor's series where the specific point on which the series…

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative. y = x2 -…

A: Given  The polynomial is  y = x2 - 4

Q: What is Taylor’s polynomial?

A: We know that an nth degree polynomial has the form Px=a0+a1x+a2x2+a3x3+……+anxn where ai's are…

Q: Q2/ A: Use Lagrange Interpolation Polynomials' to determine the relationship between the velocity of…

A: Given: Time s 10 20 60 Velocity m/s 20 120 400 To find the time t when velocity reached…

Q: Find the derivative of the function. f(x) = In(6x2 - 5x + 4) %3D

A:

Q: From the given data, identify f(4) using Newton's polynomial. (2,10), (3,15), (5,25), (8,40)

A: Explanation of the solution is given below....

Q: Question 2

A: f'(x)= 64(54x5 -27x2 ) (9x6-9x3)16

Q: Find the derivative of the function: f(x)= 16x5/4 + 8x-1/4 - 7x + 3

A:

Q: A car traveling along a straight road iIs clocked at a number of points. The data from the…

A: A) => X = (0 , 3 , 5 , 8 , 13) => F = (0 , 225 , 383 , 623 , 993) => Fs= (75 , 77 , 80 , 74…

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative. y = x2 +…

A:

Q: For a given data (x,f(x)):(-1.89,-4.179169),(0,-1),( 1.89,9.323369), estimate the function value at…

A:

Q: A car traveling along a straight road is clocked at a number of points. The data from the…

A: Given: The given table is Time 0 3 5 8 13 Distance 0 225 383 623 993 Speed 75 77 80 74 72

Q: Use the product rule to find the derivative of the following q(x) = (x-2 - x-3) (3x-1 + 4x-4)

A: To find the derivative of the function using product rule: q(x)=(x-2-x-3)(3x-1+4x-4) Solution: We…

Q: Find the third derivative of the function f(x)=8x^7/2. Simplify so there are no negative or…

A: Given query is to find the derivative if the expression.

Q: . Approximate the negative root of the function using Secant method. 3x 9x + 5x + 2 = 0

A:

Q: f (x) = x2³ (1– x) 2/3

A:

Q: Find the derivative of in two ways: first by applying the product rule and second by expanding the…

A: Applied product rule and found f'(x).

Q: Use the product rule to find the derivative of the function f ( x ) = ( x 2 - 3x + 2 ) ( 4 x 3 - x 2…

A: Given- fx=x2-3x+24x3-x2+4 To find- The derivative of the above function. Concept Used- The product…

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A:

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative.iii) y =…

A: Given: y=x3-3x2+4=(x+1)(x-2)2

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative.y = x3 -…

A: Axis interception points of x3-33x2+216x:  X Intercepts: 0, 0, 9, 0, 24, 0, Y Intercepts: 0, 0

Q: Find the 4th approximation of the positive root of the function f(x)=x4-7 using the bisection…

A: Solution

Q: Find the derivative of the function. f(x) = In(6x + 7)

A: Given that: f(x) = ln (6x+7) To find: Derivative of the given function f(x).

Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (г) — 5x — 4 2. f (x) =…

A:

Q: Find the derivative of the function using the product rule. (a) f(x) = (x3 − 2)(6x − 5) (b) f(x) =…

A: First I have written the product rule of derivative and then using it and find the required…

Q: Q1/ Use the polynomial that fits data shown by Newton divided difference ,and estimate

A:

Q: Next, differentiate the given function y = X 8x + 37 and write as a single fraction completely…

A: Derivative of function

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A: The given equation is f(x)=ex. Differentiating the given equation with respect to 'x' n-times, we…

Q: Let f (x) = 5x4 + 3x3 + 3x2 + 5x + 5. Fill in the missing coefficients for the derivative of f:

A:

Q: Use the chain rule to find the derivative of 4√10x^4+4x^8

A:

Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of the…

A:

Q: Given these data, calculate f(2.8) using Newton’s divided-difference interpolating polynomial of…

A: We know that nth order polynomial of Newton's interpolating polynomial is defined as below,…

Q: Pictured to the right is the graph of the first derivative, f'(x), of a polynomial function (x),…

A: The equation of tangent line to the curve y=fx drawn at the point x=a is  y-fa=f'ax-a⇒y=fa+x-af'a…

Q: Plot the zeros of each polynomial on a line together with thezeros of its first derivative. y = x3 -…

A: Find the zeros of a polynomial.

Q: Use the Product Rule to find the derivative of the function. f(x)= (4x+ 7)(x² 8) а. 8х b. 2x + 4 c.…

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Q: Find the second derivative of the polynomial functiony=3x4−2x3+4x2−5x+1.

A:

Q: Find the derivative of f(x)=(x2−2x)(3x+5) by first multiplying then simplify.

A: Here we have to use the concept of derivatives

Q: 3 1. 15. f(x) = 4 *+ %3D 4

A: Given,f(x)=14x+34

Q: Find the nth Maclaurin polynomial for the function f(x) = x /(x + 1), n = 4

A: