Suppose that the values of a smooth function f is known for x-0, 0.3, 0.6 and 1.2. Select the 3- point numerical differentiation scheme that will best approximate f (0.6). O Forward difference with h=D0.6 O Forward difference with h=0.3 O Backward difference with h=D0.6 Backward difference with h=0.3

Q: Let f'(x) = e*² line to the graph of the function h(x) = g(11x + 7) at x 2/īL and g(x) = f(/x). Let…

A: Solution is given below

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Q: Suppose that the values of a smooth function f is known for x=0, 0.3, 0.6 and 1.2. Select the 3-…

A: Given problem is :

Q: Suppose that f(1) = 10 and the graph of the derivative of f is shown below. 6 5 4 y = f '(x) 2 1 3…

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Q: 2ƒ(x), x = 2

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Q: Given the following graph of the derivative of the function (y f'(x)) on [-3, 9], determine the…

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Q: In the given question , find the derivatives from the left and from the right at x = 1 (if they…

A: Given that the function f(x) = | x - 1|

Q: Here is the graph of the derivative of a continuous function f: R → R. What would we see on the…

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Q: Suppose that the values of a smooth function fis known for x=0, 0.3, 1.2, 1.5 and 1.8. Select the 3…

A: According to the values given, 3-point formula for forward numerical differentiation will be useful.

Q: Let f(x) = x³ – 5x. Calculate the difference quotient ƒ(2+h)-f(2) for h h = .1 h = .01 h = -.01 h =…

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Q: Determine the second derivative of the function at x = 2 from the table shown. Round-off to four…

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Q: Suppose that the values of a smooth function fis known for x%30, 0.3, 0.6 and 1.2. Select the…

A: Use the formulas for forward and backward difference formula with h=0.3 and 0.6. The correct option…

Q: Here is the graph of the derivative of a continuous function f: R R. What would we see on the graph…

A: Given that a graph of the derivative of a continuous function f:R-->R.

Q: Suppose that the functions fand g and their derivatives with respect to x have the following values…

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Q: Suppose that the values of a smooth function f is known for x=0, 0.3, 0.6 and 1.2. Select the 3-…

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Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. Spx + 1, if x…

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Q: Determine if the following piecewise defined function is differentiable at x 0. 2х - 1, x20 f(x) =…

A: find the right-hand derivative  at x=0 limh→0+f0+h-f0h The function for x>0 is 2x-1…

Q: Determine the second derivative of the following and find the absolu extreme values for the…

A: The given function is i) g(x)=1x-1x3 ; -2.5≤x≤-1 and 0.5≤x≤1.5  for g(x)

Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >…

A: the given function is: fx=px+1     if  x≥1x2+p      if  x<1 we have to show that the given…

Q: Let f(z) = z – 6z. Calculate the difference quotient (3+h)-{(3) - for h = .1 h = .01 h = -.01 h = -1…

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Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >…

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Q: Suppose that the only information we have about a function f is that (1) and the graph of its…

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Q: Suppose that a function f(x) has derivative f' (x) = g(x)+ h(x) for some functions g(x) and h(x).…

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Q: Suppose that the values of a smooth function f is known for x= 0.3, 0.9,1.5 and 1.8. Select the 3-…

A: The values of a smooth function f is known for x= 0.3, 0.9, 1.5 and 1.8.

Q: Suppose that the following information is known about a function f: the graph of its derivative,…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Suppose that the values of a smooth function fis known for x= 0.3, 0.9,1.5 and 1.8. Select the 3-…

A: As per company guidelines, we are supposed to answer only first question in case of multiple…

Q: Consider the following function. g(x) = x2 – 2x - 4 on [0, 6] Find the derivative of the function.…

A: gx=x2-2x-4 on 0,6Derivative of function:g'(x)=2x-2Critical number:g'x=0 then x is a critical number…

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

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Q: Suppose that the values of a smooth function fis known for x-0, 0.3, 1.2, 1.5 and 1.8. Select the 3…

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Q: Suppose that the only information we have about a function f is that f(1) = 3 and the graph of its…

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Q: Consider the following function. p - 2 h(p) = p2 + 7 Find the derivative of the function. h'(p) D…

A: Given hp=p−2p2+7 Use formula  ddxfxgx=gxddxfx−fxddxgxgx2 Differentiate hp=p−2p2+7 with respect to p…

Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

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Q: Suppose h (x) =() . What is the correct result of the derivative of h with respect to x? ". In (5) A…

A: Derivative using chain rule of differentiation.

Q: Let f(x) = 33 –x The slope of the tangent line to the graph of f (=) at the point (-5, 8) is The…

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Q: Use the figure below to estimate the derivative, or state that it does not exist. The graph of f(x)…

A: Given problem is :

Q: Find the slope of the tangent line to the graph of the given function f (x) = 4x³ at the point (2,…

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Q: Suppose that the functions f and g and their derivatives with respect to x have the following values…

A: x      f(x)    g(x)     f1(x)    g1(x)      3      1      4      6     3      4…

Q: Suppose h(x) =log,(3x+1). What is the correct result Зх + %3D of the derivative of h with respect to…

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Q: Suppose you know that the equation of the tangent line to the graph of a function f at x = -2.5 is y…

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Q: Suppose that the values of a smooth function f is known for x= 0.3, 0.9,1.5 and 1.8. Select the 3-…

A: Given f is smooth function. Value known for x=0.3, 0.9, 1.5 and 1.8 We have to select the 3-point…

Q: Let f(x) = x³ – 4x. Calculate the difference quotient f(3+h)-f (3) for - h = .1 h = .01 h = –.01 h =…

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Q: Suppose that the values of a smooth function fis known for x= 0.3, 0.9,1.5 and 1.8. Select the 3-…

A: 3 points formula forward difference                                 f'(x) =-3f(x)+4f(x+h)-f(x+2h)2h…

Q: Let f(æ) = Væ + 5. Calculate the difference quotient f(31 + h) – f(31) for h h = .1 h = .01 %3D h =…

A: use the basic concept of algebra o find the quotient.

Q: Suppose that the functions fand g and their derivatives with respect to x have the following values…

A: The table is given by To evaluate: The value of the derivative of  fx+gx at x=3.

Q: Draw a graph to match the description given. F(x) has a positve derivative over (- 0,-4) and (0,8)…

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Q: Identify by color which of the graphs on the right is the derivative of the function given on the…

A: The given function was increasing before x= -0.25  So the derivative must be positive for that part…

Q: Suppose that the values of a smooth function f is known for x=0, 0.3, 0.6 and 1.2. Select the 3-…

A: The forward difference formula forward difference using the 3 point numerical differentiation is…

Q: Let f(x) 2x. Calculate the difference quotient f(3+h)–f(3) for h h = .1 h = .01 h = -.01 h = -.1 If…

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Q: Suppose that the values of a smooth function fis known for x=0, 0.3, 1.2, 1.5 and 1.8. Select the 3…

A: Clearly it is seen that 1.8 , 1.5 , 1.2 has a difference of 0.3

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: