Consider the following function. f(x) = |x2 - 16| (a) Find a formula for f'. if |x| > 0 f'(x) = if |x| < 0 For what values of x is the function not differentiable? (Enter your answers as a comma-separated list.)

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A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

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A: Consider the given piecewise function

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A: Given;. f(x)=2+|x-3| f'(x)= ?

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A: This question can be solve by taking approximation as x tends to a (more close)

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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.

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A: We will use the definition of continuity at a point to find the value of k

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A: Substitute x3 for x in the given power series of ln1+x and simplify.…

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

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A: (a) For critical points:

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A: (1) Given functions are  f(x) = (2x2-1)(x2+3)x2+1  and g(x) = (x2+8)7(2-3x2)5

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A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Q: Find all critical points of the following function. 3. 3 f(x.y)=- + 8xy

A: To find critical points of f(x, y) we find ∂f∂x and ∂f∂y then equate to zero .f(x, y ) =…

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Q: a) For the function f(x) =1-3x? , find f'(a) at a =-1 by using the definition of derivative. (a+b b)…

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Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]

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A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

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Q: 1. Find the derivative of each of the following functions a) f(x) = cos5x %3D b) g(x) = cos 5x c)…

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Q: (1) For every natural number n, x" = nx"-1 (you may use the product rule for derivatives and that x…

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

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Q: Q3. Discuss: max f(x), where f(x) = cos.x . (Start with a graph of the function, and confirm your…

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Q: (a): Find the value of k that makes function continuous at x = 4 %3D S 2x + 8 x > 4 x < 4 f(x) = 5x…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: x + 4) (2x – 1)   c) f (x) = π3   d) f (x) = 5x   e) f (x) = 4x −3/7 + 8x-1/2 + 5   f) f (x)…

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Q: 1. Use the following formula (1) to evaluate derivative for each of the functions below: f(x+ h) -…

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Q: x² +2x+1 6.) f(x) = 3

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Q: Answer the following questions for the function k(x) = x³ + x + 1: (a) The derivative at x = - is…

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: The given functions are: fx=2x2-1x2+3x2+1 and gx=x2+872-3x25 The person's brother believes that,…

Q: 1) Find the absolute extremum values of f(x) = x² – 4x + 8 over the interval [1, 4].

A: f(x) = x2 – 4x + 8