Show that the third derivatives with extended step size h is given as follows: ƒ™(x) = S(x−3h)−6ƒ (x−2h)+12ƒ (x−h)−10ƒ (x)+3ƒ (x+h) +0(h²) 2h³ where O(³) is the truncation error of the approximation. State your assumption(s).

Q: Find the values of x for which  f(x)=(1/3)x3 +(5/2)x2 +6x-17 Has a tangent line that is parallel…

A: As the line is parallel, slope of them will be equal. Slope of f(x)=x33+5x22+6x-17 will be :…

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: Find the derivative. y=(x2+x)-3 OA. dy 3x5 (2-x³) dx (1+x³)3 OB. dy_3x4 (2-x³) (1+x³)3 dx 5C 31 ...

A:

Q: The derivative of f(x) = In(5x³ – 12) Is

A:

Q: The height of a sand dune (in centimeters) is represented by f(t) = 850 - 2t² cm, where t is…

A: Given the height of the sand dune is represented by f(t)=850-2t2 cm where t is measured in years…

Q: Find an equation of the line tangent to the graph of ƒ(x) = (2x - 1) (x + 4) at (1, 5).

A: To findEquation of the line tangent to the graph y=(2x-1)(x+4)  at (1,5)⇒y=2x2+7x-4.

Q: Find an equation of the tangent line to the graph of f at the point  (2, f(2)). f(x) = 3(6x − 2)4…

A: The given function is f(x) = 3(6x-2)4The slope m is obtained.

Q: Find the derivative of the function. f(t) = (7t² - 4t + 1)3/2 21t – 6 f 't) = 7? – 41+ 1)² (72 – 4t…

A:

Q: Find the derivatives of the functions in Exercis

A: The given function is q=2r-r23.

Q: The equation of the tangent line for the function f(x) = -3 – 6x at r = 6 is %3D

A: The given function is, fx=-3-6x We need to find the equation of the tangent line to the function at…

Q: Find the derivative of y with respect to x if y = (8x2 - 16x + 16) ex. dy dx =

A: y=8x2-16x+16ex

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: Find the derivative of f (t) = (6t3³ - 8t² + 7) 46 f' (t) = BA

A: Given query is to find indicated derivative.

Q: I. Find the derivative of the following. Show that the applicable differentiat rules has been used.…

A:

Q: f(x) = 4√x + 2x1/2 – 8x-7/8 + x2 1 23 +2

A: The given function is fx=4x+2x12-8x-78+x2-1x3+2. Find the derivative of the given function. Here we…

Q: Find the derivative of y = f(r) = VI(3r + ²). x(3x+x %3D

A:

Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Assume that ƒ′(3) = -1, g′(2) = 5, g(2) = 3, and y = ƒ(g(x)). What is y′ at x = 2?

A: Given:

Q: I. Find the derivatives of the following functions: 4. -3xy? + 5x²y² = 2x² %3D

A:

Q: I. Find the derivative of the following functions: a. f(r) = 23 + 6x b. h(r) = (3r + 4)2 c. y = Vr3

A: According to company rules, I need to solve first 3 subparts when multiple subparts are posted