For the function given in the below table, ,5 The approximation of f(x) dx using Mid – Point Rule is 3 5 f(x) 2 2.5 3 3.5 4.

Q: Consider the following function. f(x) = −x2 − 6x − 6 Find its average rate of change over the…

A: Solution : According to the question,     The average rate of change of the function f(x) over an…

Q: Find a formula for df 1 dx for the function below using the Derivative Rule for Inverses. f(x) = (5…

A: Given,         fx=5-3x3We know that,           The Derivative Rule for inverses is given by…

Q: The derivative of a function f(x) at a particular value of x can be approximately calculated by f(x)…

A: The given function is f(x)=7e0.5x.

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: For n 4 we find the derivative of f(x) = x* as follows: f(x + h) - f(x) (x + h)* – x lim f'(x) = lim…

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Q: What is the derivative of f(x) = Select the correct answer below: O 4V/2 O 2012 3 O w/s O 16V/2 о 3…

A: Derivative of function f(x)=43x54 at x=4

Q: 1. Use the function f (x) = x² – 3 to answer the following questions" A. Find the average rate of…

A: Given: f(x)=x2-3

Q: find the requested higher-order derivative for the given function... d2y/dx2 of y=3sinx +x2cosx

A: Given: y=3sinx+x2cosx The objective is to find the higher-order derivative d2ydx2 Let's find the…

Q: The actual error when the first derivative of f(x) = x - 3ln x at x = 3 is approximated by the…

A: Solution:-

Q: 4. Given that g(x) = x^4 + x^3 − 3x^2 + 2, answer the following. (a)  g"(x) =  .............. (b)…

A: We have,  gx=x4+x3-3x2+2              ⋯⋯1 (a) By definition of derivative, ddxkxn=knxn-1 On…

Q: The second derivative for the following function at x = 2 f(x) = v2x + is O 1 O 1/4 O 1/2 O 3/4

A: Use the basis concept of integration and derivative than simplify.

Q: What is the first derivative of f (x) = ln n A)? 3x²+7x 5х Select the correct answer below: бх-7 O…

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

Q: The function g is differentiable, and the tangent line to the graph of y = g(x) at x = -4 is y = 5x…

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Q: For the function f(x) = 2* we use the two-point formula to approximate the first derivative of f at…

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Q: ) f(t) = t2-2

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Q: Consider the following function. f(x) = x2 + 4x − 5 Find the average rate of change of the function…

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Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Given functions are: y=a2-t2x=42t2+a In order to calculate d2ydx2, firstly we will calculate d2ydt2…

Q: Consider the following function. F{x) = x3/2 Find its average rate of change over the interval [4,…

A: (a). The expression for the average rate of change over the interval [a,b] is: ∆y∆x=fb-fab-a Given:…

Q: The second derivative for the following function at x = 2 f(x) = V2x + is O 1 O 1/4 O 1/2 3/4

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Q: If f(x) is a differentiable function such that f(6) = f'(6) = 2, compute the following derivative. d…

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Q: Q1. Integrate the following functions with respect to x: y = 3x2 (1+x³)*

A: Explanation of the answer is as follows

Q: Find the derivative of the following functions by applying "Delta Method". Show your complete…

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Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

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

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Q: The graph of a function f is given. YA Estimate 10 [20 1 0 1 f(x) dx using five subintervals with…

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Q: Q3. Derive the following formula for approximating the derivative f": ƒ™" (x) ≈ (f(x +3h) − 3f (x +…

A: To Derive: f'''(x)≈1h3f(x+3h)-3f(x+2h)+3f(x+h)-f(x). To find: Big-Oh error term from the above…

Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

A:

Q: The cost, in thousands of dollars, of airing X 30-second television commercials during a Super Bowl…

A: Note:- These are multiple sub parts question and according to our company guideline we can do…

Q: Find the approximate value of second derivative f"(0) with the step h for the following function by…

A:

Q: Suppose that the first derivative of f(x) = is approximated by the following formula 2x+2 F'e…

A: The given problem is to find the actual error of the first derivative of function at x=1 using the…

Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Find the derivative of the following functions using the long method (limits) (a) x = t* – 5t – 3…

A: (a) Consider the equation x=f(t)=12t4-5t-3 To find the derivative of this using the limits.  So we…

Q: 2.) f(x) = (x5 – 2x³ + 1) 3

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Q: please find h'(1) based of given h(x)=f(g(x))

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Q: Find the average rate of change of f(x)=3x^2−9 on the interval [1,t].  (answer with an expression…

A: We have to find average rate of change of f(x) on the interval [1,t]

Q: Q2. Derive the following formula for approximating the derivative f": ƒ"(x) ≈ : (-f(x+2h) +16f(r+h)-…

A: To show:- f''x ≈112h2  -fx+2h + 16 f(x+h) -30 f(x) +16 f(x-h) - f(x-2h)

Q: Suppose the linear approximation for a function f(x) at a = 3 is given by the tangent line y -2x +…

A: The given functions are

Q: 2 The linear approximation for the function f(x) = be used to estimate f(0.01). Which of the…

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Q: Find the approximate value of derivative f'(0) with the step size h for the following function by…

A:

Q: Consider the following function. f(x) = x2 + 4x − 5 Find the average rate of change of the function…

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Q: 1 Is the function given by f(x) = ) 5x+1, for x s5, continuous at x= 5? Why or why not? %3D 5x- 19,…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: The average value of the function f(x)=x² on the interval [0 , b] is 12 What is the value of b ?…

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Q: Find the approximate value of derivative f(0) with the step size h for the following function by…

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Q: Find the derivative. y= e at O 4(1/4)x -4(5/4)x In 4 4(3/4)x In 4 4(5/4)x 25 n4 16

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Q: 4) /() =2-2 3. 5) y = x*+2x+1 6.) f(x) =

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Q: Suppose ƒ is an even function and Evaluate

A: Given f is an even function, ∫-88f(x)dx=18

Q: What is the first derivative with respect to x of the function g(x)= 4/9 * О 4/9 O 4 O 12

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Q: 8.) f(x) = v5x6 – 12 10.) f(x) = (x - 4x- 7)

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Q: The actual error when the first derivative of f(x) = x-2lnx at x = 2 is approximated by the…

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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: