The function f (x) is defined by the rule x2 +1 if x < 2 f (x) = if x = 2 %3D 4x – 3 if x > 2 - a) Calculate the left derivative and the right derivative of f at x = 2. You must use the limit definition because we did not establish rules for calculating one sided derivatives. b) Write a piecewise function for the derivative of f at all points in R.

Q: The graph of the derivative of f is shown below: -y-5 4 -3 -2- -1- 0 1 2 f'(x) 3 4 f', the…

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Q: (a) tive of f(r) = r at z = a. Find the value of a given that lim, 8+h)* – 64 represents the deriva-…

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Q: Given the function, find the derivative f (x) = -()" 3z 4 3z- 3 12() 3z-4 O None of the Above

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Q: use the second derivative test to find the local exterma of the function f(x) =x3 -9x2-48x+72 on R

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Q: The function f(z) is analytic if

A: analytic functions are functions which are locally given by the convergent power series. i.e any…

Q: h) f(x) = Write your answer in simplified factored form. %3D

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Q: Suppose that f is a function given as f(x) = -3x² - 2x - 3. Simplify the expression f(x + h). f(x +…

A: f(x)=-3x2-2x-3(i) f(x+h)=-3(x+h)2-2(x+h)-3

Q: Q1) By using transformations of mother functions, sketch the following curves and determine the…

A: We will find out the required values.

Q: Find the derivative using the formal definition f (x) = 3x2- 4x – 2

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Q: Determine if the function f (z) = y + xi is analytic. you must show detailed work

A: we have to check if the function  f(z)=y+xi

Q: Identify the original function f(x) and what value of c to evaluate f'(c). (3x-9x²)+(42) x+2 lim…

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Q: Consider the function 2x + 1 g(x) = x +1 a) Evaluate the derivative of the function. b) Sketch the…

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Q: 16. f(x) = 3x2+36x+108 step 1 f(x + Ax): step 2 f(x + Ax) - f(x) f(x + Ax)-f(x) step 3 Ax f(x + Ax)-…

A: The differentiation of the a function can be obtained using the numerical differentiation. This can…

Q: Determine all values of x for which the slope of the line tangent to y=x³ - 4x² +9x-1 is 5.

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Q: 2.) State one of the two formulas for finding the derivative of a function f(x) that uses limits.…

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