Consider the function f(x) = 6x + 12 sin x on the domain [0, 2π]. Use analytic techniques (calculus, algebra, trigonometry) to determine the intervals where the function is increasing and decreasing. Use exact values in your response. f(x) is increasing on f(x) is decreasing on

Q: 62²(2³-128) (³+64)³ Consider the function f and its derivatives f(x)=3+64 f'(x)= -2(³-32) (+64)2…

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Q: Differentiate the function In x f(x) = In 2x +3, x>0

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Q: Where is the function f(x) =| x | differentiable?

A: Given information: fx=x The function, after removing modulus function, y=x=x,      x>0=-x,…

Q: Find the derivative the following functions. a) h(x) = 4√√x+3x8 +5ex + π² x³-6x²+8x b) g(x) x²-2x =

A: The given functions are The aim is to find the derivative of the given functions.

Q: Let f be the function given by f(x)=√x² - 9x² Find f'(x).

A: Formula Given function

Q: By carefully showing all your steps, differentiate the function f(x) = (tan−¹(x + √√x)) 4

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Q: 4x2-9x+2 Find a functionf such that f'(x) = and f(1) = 0. %3D

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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: Let R+ = {x € R|x>0} be the set of positive real numbers. Let A = [a,b), a,beRb +00, be an (right…

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Q: Let f(x) = 7/2x -6. For what value of x does function f have the given value?  f(x) = 2/3 X= ?

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Q: Can f(z) = | Re (z2) | + i.Im (-z) be derived from the function z=0? Show it.

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Q: 3 s(1) =v° (v* + 2v=1) f(v) =

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Q: et y = f(x) = (4√x + 6) (6√x+8) (7√x+6). Find the derivative function f(x) and evaluate it at x = 1.…

A: We have to find the derivative