a) Find a second degree polynomial approximating the function f(x)= Inx , and passing from the points (1, f(1)),(2, ƒ(2)) and (4, f(4)). b) Approximate ƒ(2.5) using the polynomial in part (a) E,(x)= (x-xo)(x-x,)(x-x2)...(x- xx) (N+1)! c) use the error formula to estimate the error at x=2.5

Q: Consider the function y = (a) Find the x- and y-intercepts of f(x)

A: An x-intercept of a function f(x) is a point on the x-axis at which the graph of the function f(x)…

Q: The first derivative, f'(x), of a polynomial function f(x) is given below. Use this derivative to…

A:

Q: Identify and sketch the domain of f(x, y) = y² + 4x + 2 In(1-x² - y²)

A:

Q: Find f′(9) if f(x)=7x2 +5x+5/ √x

A: To find f'(9) , initially we have to find f'(x) from the given f(x) then substitute x=9 in the…

Q: f(x) = -9 f'(x) = -(x²+9) (x²-9)2 f"(x) = 2x(x²+27) (x²–9)3 4. Given a) Provide a complete analysis…

A: a)

Q: 2) Find the fixed point of the functions : A. f(x) = x² + 5x + 3 B. f(x) = x³ – 4x² + 6x – 2 C. f(x)…

A:

Q: The curve represented by r(t) = f(t)i + g(t)j + h(t)k is a line. Are f, g, and h first-degree…

A:

Q: 1 >Use the following models to consider the function f(x)=; on the interval 1+x? [-5,5]. (1)…

A: The function given is as follows: fx=11+x2 (1) We are asked to find the interpolating polynomial of…

Q: Determine whether the functions f1(x) := x + 1; f2(x) := sin(x); f3(x) := x - 1; f4(x) := 3 are…

A:

Q: 2. What is Pia first-degree polynomial function whose value and slope agree with the value and slope…

A: “Since you have asked multiple questions, as per authoring guidelines we will solve the first…

Q: Find a first-degree polynomial function P₁ whose value and slope agree with the value and slope of…

A: The given function .The objective is to find the polynomial function  whose value and slope agree…

Q: The curves of three polynomials that are related to each other through differentiation of the…

A: Here we will going  to use relation between f(x) ,f'(x) and f''(x) to identify a graph of a function…

Q: Suppose a Curve passes through the faints (0,-4), (0.6,-3.64) and (1,-3). Find the polynomial which…

A: To find the best fit to the given point and find the value of function at x=-3.5

Q: Find the linear function f(x) passing through (6,8) and (8,10) Enter answer in form…

A: Explanation of the answer is as follows

Q: Find f(g()) and g(f(2)) for the pair of functions. f() =+1 g(2) 34x-17 flo(2)) = %3D 9(f(=)) = %3D

A: Given, f(x) = x + 1  g(x) = 4x - 17

Q: On which interval is the function f(x) = x2 - 2x - 8 decreasing? A [-2, 4] B (-∞, 4) C…

A: Given, f(x) = x2 - 2x - 8

Q: Assume that the function f is a one-to-one function. (a) If f(5) = 2, find f-'(2). Your answer is…

A: Given that to he function f is one-to-one function.

Q: Find the following using the rule indicated (only): i) If f(x) = (6x? – 8) (3x + 2), find f'(3)…

A:

Q: Derive a 2nd order accurate finite difference expression for the first derivative at point i-1,…

A:

Q: Determine whether the pairs of the functions are linearly inde- pendent or linearly dependent on the…

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

Q: Find a polynomial f with the following properties: i) f is concave up on (-, –2) U (0, ∞) and…

A: Function and derivative

Q: (a) Graph the IL f(x) = in the viewi (b) Using the g a rough ske Example 2. (c) Calculatef Compare w

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: